The Quran contains at least 109 verses that speak of war with nonbelievers, usually on the basis of their status as non-Muslims. Some are quite graphic, with commands to chop off heads and fingers and kill infidels wherever they may be hiding. Muslims who do not join the fight are called 'hypocrites' and warned that Allah will send them to Hell if they do not join the slaughter.
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, who were led meekly to the slaughter. These Muslims are killed in battle as they attempt to inflict death and destruction for the cause of Allah. This is the theological basis for today's suicide bombers.
Quran (4:76) - "Those who believe fight in the cause of Allah…"