These are by no means all the verses in the Qu'ran or the Hadith, just a good representation.
Quran (2:191-193) - "And slay them wherever ye find them, and drive them out of the places whence they drove you out, for persecution [of Muslims] is worse than slaughter [of non-believers]... but if they desist, then lo! Allah is forgiving and merciful. And fight them until persecution is no more, and religion is for Allah." The historical context of this passage is not defensive warfare, since Muhammad and his Muslims had just relocated to Medina and were not under attack by their Meccan adversaries. In fact, the verses urge offensive warfare, in that Muslims are to drive Meccans out of their own city (which they later did). The use of the word "persecution" by some Muslim translators is thus disingenuous (the actual Muslim words for persecution - "idtihad" - and oppression - a variation of "z-l-m" - do not appear in the verse). The actual Arabic comes from "fitna" which can mean disbelief, or the disorder that results from unbelief or temptation. Taken as a whole, the context makes clear that violence is being authorized until "religion is for Allah" - ie. unbelievers desist in their unbelief.
Quran (2:244) - "Then fight in the cause of Allah, and know that Allah Heareth and knoweth all things."
Quran (2:216) - "Fighting is prescribed for you, and ye dislike it. But it is possible that ye dislike a thing which is good for you, and that ye love a thing which is bad for you. But Allah knoweth, and ye know not." Not only does this verse establish that violence can be virtuous, but it also contradicts the myth that fighting is intended only in self-defense, since the audience was obviously not under attack at the time. From the Hadith, we know that this verse was narrated at a time that Muhammad was actually trying to motivate his people into raiding merchant caravans for loot.
Quran (3:56) - "As to those who reject faith, I will punish them with terrible agony in this world and in the Hereafter, nor will they have anyone to help."
Quran (3:151) - "Soon shall We cast terror into the hearts of the Unbelievers, for that they joined companions with Allah, for which He had sent no authority". This speaks directly of polytheists, yet it also includes Christians, since they believe in the Trinity (ie. what Muhammad incorrectly believed to be 'joining companions to Allah').
Quran (4:74) - "Let those fight in the way of Allah who sell the life of this world for the other. Whoso fighteth in the way of Allah, be he slain or be he victorious, on him We shall bestow a vast reward." The martyrs of Islam are unlike the early Christians, led meekly to the slaughter. These Muslims are killed in battle, as they attempt to inflict death and destruction for the cause of Allah. Here is the theological basis for today's suicide bombers.
Quran (4:76) - "Those who believe fight in the cause of Allah…"
Quran (4:89) - "They but wish that ye should reject Faith, as they do, and thus be on the same footing (as they): But take not friends from their ranks until they flee in the way of Allah (From what is forbidden). But if they turn renegades, seize them and slay them wherever ye find them; and (in any case) take no friends or helpers from their ranks."
Quran (4:95) - "Not equal are those believers who sit (at home) and receive no hurt, and those who strive and fight in the cause of Allah with their goods and their persons. Allah hath granted a grade higher to those who strive and fight with their goods and persons than to those who sit (at home). Unto all (in Faith) Hath Allah promised good: But those who strive and fight Hath He distinguished above those who sit (at home) by a special reward,-" This passage criticizes "peaceful" Muslims who do not join in the violence, letting them know that they are less worthy in Allah's eyes. It also demolishes the modern myth that "Jihad" doesn't mean holy war in the Quran, but rather a spiritual struggle. Not only is the Arabic word used in this passage, but it is clearly not referring to anything spiritual, since the physically disabled are given exemption. (The Hadith reveals the context of the passage to be in response to a blind man's protest that he is unable to engage in Jihad and this is reflected in other translations of the verse).
Quran (4:104) - "And be not weak hearted in pursuit of the enemy; if you suffer pain, then surely they (too) suffer pain as you suffer pain..." Is pursuing an injured and retreating enemy really an act of self-defense?
Quran (5:33) - "The punishment of those who wage war against Allah and His messenger and strive to make mischief in the land is only this, that they should be murdered or crucified or their hands and their feet should be cut off on opposite sides or they should be imprisoned; this shall be as a disgrace for them in this world, and in the hereafter they shall have a grievous chastisement"
Quran (8:12) - "I will cast terror into the hearts of those who disbelieve. Therefore strike off their heads and strike off every fingertip of them" No reasonable person would interpret this to mean a spiritual struggle.
Quran (8:15) - "O ye who believe! When ye meet those who disbelieve in battle, turn not your backs to them. (16)Whoso on that day turneth his back to them, unless maneuvering for battle or intent to join a company, he truly hath incurred wrath from Allah, and his habitation will be hell, a hapless journey's end."
Quran (8:39) - "And fight with them until there is no more fitna (disorder, unbelief) and religion should be only for Allah" Some translations interpret "fitna" as "persecution", but the traditional understanding of this word is not supported by the historical context (See notes for 2:293, also). The Meccans were simply refusing Muhammad access to their city during Haj. Other Muslims were allowed to travel there - just not as an armed group, since Muhammad had declared war on Mecca prior to his eviction. The Meccans were also acting in defense of their religion, since it was Muhammad's intention to destroy their idols and establish Islam by force (which he later did). Hence the critical part of this verse is to fight until "religion is only for Allah", meaning that the true justification of violence was the unbelief of the opposition. According to the Sira (Ibn Ishaq/Hisham 324) Muhammad further explains that "Allah must have no rivals."
Quran (8:57) - "If thou comest on them in the war, deal with them so as to strike fear in those who are behind them, that haply they may remember."
Quran (8:59-60) - "And let not those who disbelieve suppose that they can outstrip (Allah's Purpose). Lo! they cannot escape. Make ready for them all thou canst of (armed) force and of horses tethered, that thereby ye may dismay the enemy of Allah and your enemy."
Quran (8:65) - "O Prophet, exhort the believers to fight..."
Quran (9:5) - "So when the sacred months have passed away, then slay the idolaters wherever you find them, and take them captive and besiege them and lie in wait for them in every ambush, then if they repent and keep up prayer and pay the poor-rate, leave their way free to them." According to this verse, the best way of staying safe from Muslim violence is to convert to Islam (prayer (salat) and the poor tax (zakat) are among the religion's Five Pillars). This popular claim that the Quran only inspires violence within the context of self-defense is seriously challenged by this passage as well, since the Muslims to whom it was written were obviously not under attack. Had they been, then there would have been no waiting period (earlier verses make it a duty for Muslims to fight in self-defense, even during the sacred months).
Quran (9:14) - "Fight them, Allah will punish them by your hands and bring them to disgrace..."
Quran (9:20) - "Those who believe, and have left their homes and striven with their wealth and their lives in Allah's way are of much greater worth in Allah's sight. These are they who are triumphant." The Arabic word interpreted as "striving" in this verse is the same root as "Jihad". The context is obviously holy war.
Quran (9:29) - "Fight those who believe not in Allah nor the Last Day, nor hold that forbidden which hath been forbidden by Allah and His Messenger, nor acknowledge the religion of Truth, (even if they are) of the People of the Book, until they pay the Jizya with willing submission, and feel themselves subdued." "People of the Book" refers to Christians and Jews. According to this verse, they are to be violently subjugated, with the sole justification being their religious status. This was one of the final "revelations" from Allah and it set in motion the tenacious military expansion, in which Muhammad's companions managed to conquer two-thirds of the Christian world in the next 100 years. Islam is intended to dominate all other people and faiths.
Quran (9:30) - "And the Jews say: Ezra is the son of Allah; and the Christians say: The Messiah is the son of Allah; these are the words of their mouths; they imitate the saying of those who disbelieved before; may Allah destroy them; how they are turned away!"
Quran (9:38-39) - "O ye who believe! what is the matter with you, that, when ye are asked to go forth in the cause of Allah, ye cling heavily to the earth? Do ye prefer the life of this world to the Hereafter? But little is the comfort of this life, as compared with the Hereafter. Unless ye go forth, He will punish you with a grievous penalty, and put others in your place." This is a warning to those who refuse to fight, that they will be punished with Hell.
Quran (9:41) - "Go forth, light-armed and heavy-armed, and strive with your wealth and your lives in the way of Allah! That is best for you if ye but knew." See also the verse that follows (9:42) - "If there had been immediate gain (in sight), and the journey easy, they would (all) without doubt have followed thee, but the distance was long, (and weighed) on them" This contradicts the myth that Muslims are to fight only in self-defense, since the wording implies that battle will be waged a long distance from home (in another country and on Christian soil, in this case, according to the historians).
Quran (9:73) - "O Prophet! strive hard against the unbelievers and the hypocrites and be unyielding to them; and their abode is hell, and evil is the destination." Dehumanizing those who reject Islam, by reminding Muslims that they are merely firewood for Hell, makes it easier to justify slaughter. It also explains why today's devout Muslims have little regard for those outside the faith.
Quran (9:88) - "But the Messenger, and those who believe with him, strive and fight with their wealth and their persons: for them are (all) good things: and it is they who will prosper."
Quran (9:111) - "Allah hath purchased of the believers their persons and their goods; for theirs (in return) is the garden (of Paradise): they fight in His cause, and slay and are slain: a promise binding on Him in truth, through the Law, the Gospel, and the Quran: and who is more faithful to his covenant than Allah? then rejoice in the bargain which ye have concluded: that is the achievement supreme."
Quran (9:123) - "O you who believe! fight those of the unbelievers who are near to you and let them find in you hardness."
Quran (17:16) - "And when We wish to destroy a town, We send Our commandment to the people of it who lead easy lives, but they transgress therein; thus the word proves true against it, so We destroy it with utter destruction." Note that the crime is moral transgression, and the punishment is "utter destruction." (Before ordering the 9/11 attacks, Osama bin Laden first issued Americans an invitation to Islam).
Quran (18:65-81) - This parable lays the theological groundwork for honor killings, in which a family member is murdered because they brought shame to the family, either through apostasy or perceived moral indiscretion. The story (which is not found in any Jewish or Christian source) tells of Moses encountering a man with "special knowledge" who does things which don't seem to make sense on the surface, but are then justified according to later explanation. One such action is to murder a youth for no apparent reason (74). However, the wise man later explains that it was feared that the boy would "grieve" his parents by "disobedience and ingratitude." He was killed so that Allah could provide them a 'better' son. (Note: This is one reason why honor killing is sanctioned by Sharia. Reliance of the Traveler (Umdat al-Saliq) says that punishment for murder is not applicable when a parent or grandparent kills their offspring (o.1.1-2).)
Quran (21:44) - "We gave the good things of this life to these men and their fathers until the period grew long for them; See they not that We gradually reduce the land (in their control) from its outlying borders? Is it then they who will win?"
Quran (25:52) - "Therefore listen not to the Unbelievers, but strive against them with the utmost strenuousness..." "Strive against" is Jihad - obviously not in the personal context. It's also significant to point out that this is a Meccan verse.
Quran (33:60-62) - "If the hypocrites, and those in whose hearts is a disease, and the alarmists in the city do not cease, We verily shall urge thee on against them, then they will be your neighbors in it but a little while. Accursed, they will be seized wherever found and slain with a (fierce) slaughter." This passage sanctions the slaughter (rendered "merciless" and "horrible murder" in other translations) against three groups: Hypocrites (Muslims who refuse to "fight in the way of Allah" (3:167) and hence don't act as Muslims should), those with "diseased hearts" (which include Jews and Christians 5:51-52), and "alarmists" or "agitators who include those who merely speak out against Islam, according to Muhammad's biographers. It is worth noting that the victims are to be sought out by Muslims, which is what today's terrorists do. If this passage is meant merely to apply to the city of Medina, then it is unclear why it is included in Allah's eternal word to Muslim generations.
Quran (47:3-4) - "Those who reject Allah follow vanities, while those who believe follow the truth from their lord. Thus does Allah set forth form men their lessons by similitude. Therefore when you meet in battle those who disbelieve, then smite the necks until when you have overcome them, then make (them) prisoners," Those who reject Allah are to be subdued in battle. The verse goes on to say the only reason Allah doesn't do the dirty work himself is in order to to test the faithfulness of Muslims. Those who kill pass the test. "But if it had been Allah's Will, He could certainly have exacted retribution from them (Himself); but (He lets you fight) in order to test you, some with others. But those who are slain in the Way of Allah,- He will never let their deeds be lost."
Quran (47:35) - "Be not weary and faint-hearted, crying for peace, when ye should be uppermost (Shakir: "have the upper hand") for Allah is with you,"
Quran (48:17) - "There is no blame for the blind, nor is there blame for the lame, nor is there blame for the sick (that they go not forth to war). And whoso obeyeth Allah and His messenger, He will make him enter Gardens underneath which rivers flow; and whoso turneth back, him will He punish with a painful doom." Contemporary apologists sometimes claim that Jihad means 'spiritual struggle.' Is so, then why are the blind, lame and sick exempted? This verse also says that those who do not fight will suffer torment in hell.
Quran (48:29) - "Muhammad is the messenger of Allah. And those with him are hard (ruthless) against the disbelievers and merciful among themselves" Islam is not about treating everyone equally. There are two very distinct standards that are applied based on religious status. Also the word used for 'hard' or 'ruthless' in this verse shares the same root as the word translated as 'painful' or severe' in verse 16.
Quran (61:4) - "Surely Allah loves those who fight in His way" Religion of Peace, indeed! This is followed by (61:9): "He it is who has sent His Messenger (Mohammed) with guidance and the religion of truth (Islam) to make it victorious over all religions even though the infidels may resist."
Quran (61:10-12) - "O ye who believe! Shall I lead you to a bargain that will save you from a grievous Penalty?- That ye believe in Allah and His Messenger, and that ye strive (your utmost) in the Cause of Allah, with your property and your persons: That will be best for you, if ye but knew! He will forgive you your sins, and admit you to Gardens beneath which Rivers flow, and to beautiful mansions in Gardens of Eternity." This verse was given in battle. It uses the Arabic word, Jihad.
Quran (66:9) - "O Prophet! Strive against the disbelievers and the hypocrites, and be stern with them. Hell will be their home, a hapless journey's end." The root word of "Jihad" is used again here. The context is clearly holy war, and the scope of violence is broadened to include "hypocrites" - those who call themselves Muslims but do not act as such.
From the Hadith:
Bukhari (52:177) - Allah's Apostle said, "The Hour will not be established until you fight with the Jews, and the stone behind which a Jew will be hiding will say. "O Muslim! There is a Jew hiding behind me, so kill him."
Bukhari (52:256) - The Prophet... was asked whether it was permissible to attack the pagan warriors at night with the probability of exposing their women and children to danger. The Prophet replied, "They (i.e. women and children) are from them (i.e. pagans)." In this command, Muhammad establishes that it is permissible to kill non-combatants in the process of killing a perceived enemy. This provides justification for the many Islamic terror bombings.
Bukhari (52:220) - Allah's Apostle said... 'I have been made victorious with terror'
Abu Dawud (14:2526) - The Prophet (peace_be_upon_him) said: Three things are the roots of faith: to refrain from (killing) a person who utters, "There is no god but Allah" and not to declare him unbeliever whatever sin he commits, and not to excommunicate him from Islam for his any action; and jihad will be performed continuously since the day Allah sent me as a prophet until the day the last member of my community will fight with the Dajjal (Antichrist)
Abu Dawud (14:2527) - The Prophet said: Striving in the path of Allah (jihad) is incumbent on you along with every ruler, whether he is pious or impious
Muslim (1:33) - the Messenger of Allah said: I have been commanded to fight against people till they testify that there is no god but Allah, that Muhammad is the messenger of Allah
Bukhari (8:387) - Allah's Apostle said, "I have been ordered to fight the people till they say: 'None has the right to be worshipped but Allah'. And if they say so, pray like our prayers, face our Qibla and slaughter as we slaughter, then their blood and property will be sacred to us and we will not interfere with them except legally."
Muslim (1:30) - "The Messenger of Allah said: I have been commanded to fight against people so long as they do not declare that there is no god but Allah."
Bukhari (11:626) - [Muhammad said:] "I decided to order a man to lead the prayer and then take a flame to burn all those, who had not left their houses for the prayer, burning them alive inside their homes."
Muslim (1:149) - "Abu Dharr reported: I said: Messenger of Allah, which of the deeds is the best? He (the Holy Prophet) replied: Belief in Allah and Jihad in His cause..."
Muslim (20:4645) - "...He (the Messenger of Allah) did that and said: There is another act which elevates the position of a man in Paradise to a grade one hundred (higher), and the elevation between one grade and the other is equal to the height of the heaven from the earth. He (Abu Sa'id) said: What is that act? He replied: Jihad in the way of Allah! Jihad in the way of Allah!"
Muslim (20:4696) - "the Messenger of Allah (may peace be upon him) said: 'One who died but did not fight in the way of Allah nor did he express any desire (or determination) for Jihid died the death of a hypocrite.'"
Muslim (19:4321-4323) - Three separate hadith in which Muhammad shrugs over the news that innocent children were killed in a raid by his men against unbelievers. His response: "They are of them (meaning the enemy)."
Muslim (19:4294) - "When the Messenger of Allah (may peace be upon him) appointed anyone as leader of an army or detachment he would especially exhort him... He would say: Fight in the name of Allah and in the way of Allah. Fight against those who disbelieve in Allah. Make a holy war... When you meet your enemies who are polytheists, invite them to three courses of action. If they respond to any one of these, you also accept it and withhold yourself from doing them any harm. Invite them to (accept) Islam; if they respond to you, accept it from them and desist from fighting against them... If they refuse to accept Islam, demand from them the Jizya. If they agree to pay, accept it from them and hold off your hands. If they refuse to pay the tax, seek Allah's help and fight them.
Tabari 7:97 The morning after the murder of Ashraf, the Prophet declared, "Kill any Jew who falls under your power." Ashraf was a poet, killed by Muhammad's men because he insulted Islam. Here, Muhammad widens the scope of his orders to kill. An innocent Jewish businessman was then slain by his Muslim partner, merely for being non-Muslim.
Tabari 9:69 "Killing Unbelievers is a small matter to us" The words of Muhammad, prophet of Islam.
Tabari 17:187 "'By God, our religion (din) from which we have departed is better and more correct than that which these people follow. Their religion does not stop them from shedding blood, terrifying the roads, and seizing properties.' And they returned to their former religion." The words of a group of Christians who had converted to Islam, but realized their error after being shocked by the violence and looting committed in the name of Allah. The price of their decision to return to a religion of peace was that the men were beheaded and the woman and children enslaved by the caliph Ali.
Ibn Ishaq/Hisham 327: - “Allah said, ‘A prophet must slaughter before collecting captives. A slaughtered enemy is driven from the land. Muhammad, you craved the desires of this world, its goods and the ransom captives would bring. But Allah desires killing them to manifest the religion.’”
Ibn Ishaq/Hisham 990: - Lest anyone think that cutting off someone's head while screaming 'Allah Akbar!' is a modern creation, here is an account of that very practice under Muhammad, who seems to approve.
Ibn Ishaq/Hisham 992: - "Fight everyone in the way of Allah and kill those who disbelieve in Allah." Muhammad's instructions to his men prior to a military raid.
Sahih Muslim book 41, no. 6985 "The prophet, prayer and peace be upon him, said: The time [of judgment] will not come until Muslims will fight the Jews and kill them; until the Jews hide behind rocks and trees, which will cry: O Muslim! There is a Jew hiding behind me, come on and kill him!"
Don't take my word for it, read the Qu'ran yourself.