Al Zarqawi said it in his speeches. Bin Laden said it in his as well. All that has to happen is for someone to be declared takfir (an infidel or unbeliever), then it is permitted to kill them, assuring your place in Heaven. Check it out for yourself. Many of the quotes from the Qur'an are taken out of context, but some are blatant (as pointed out by Spuds). You must look at it not with Western eyes, but from a Middle Eastern Perspective. They have been killing each other for thousands of years with no signs of actually finding peace. We can't understand that. Do a little research, but to help you out:
Consider Sura 5:33 -
"The only reward of those who make war upon Allah and His messenger and strive after corruption in the land will be that they will be killed or crucified, or have their hands and feet on alternate sides cut off, or will be expelled out of the land. Such will be their degradation in the world, and in the Hereafter,"
Keeping in mind that those who "make war" might also include civilized disagreement or discussion (again, don't look at it with a Western mentality). Thus, anyone that disagrees with or is against Islam. Also Sura 47:4 -
"Now when ye meet in battle those who disbelieve, then it is smiting of the necks until, when ye have routed them, then making fast of bonds; and afterward either grace or ransom till the war lay down its burdens..."
Again remembering that to the Muslim, "the battle" is not just a battlefield, but where ever they may choose to take it. This is why many Christian missionary villages have faced "ethnic cleansing" in Africa, not because they engaged in battle with Muslims, but because Muslim leaders brought the battle to them.
They view it as a duty, much the same way that it is a duty for the Christian to "love their enemies" and to "pray for those that persecute them" (Matt 5:44). They do what they do because they read the Qur'an and obey it.