Quran (25:52) - "Therefore listen not to the Unbelievers, but strive against them with the utmost strenuousness with it." - The root for Jihad is used twice in this verse - although it may not have been referring to Holy War when narrated, since it was prior to the hijra at Mecca. The "it" at the end is thought to mean the Quran. Thus the verse may have originally meant a non-violent resistance to the 'unbelievers.' Obviously, this changed with the hijra. 'Jihad' after this is almost exclusively within a violent context. The enemy is always defined as people, rather than ideas.
Quran (33:60-62) - "If the hypocrites, and those in whose hearts is a disease (evil desire for adultery, etc.), and those who spread false news among the people in Al-Madinah, cease not, We shall certainly let you overpower them, then they will not be able to stay in it as your neighbors but a little while Accursed, wherever found, they shall be seized and killed with a (terrible) slaughter." This passage sanctions slaughter (rendered as "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 - those who speak out against Islam. It is worth noting that the victims are to be sought out, which is what today's terrorists do.
Quran (47:3-4) - "Those who disbelieve follow falsehood, while those who believe follow the truth from their Lord… So, when you meet (fighting Jihad in Allah's Cause), those who disbelieve smite at their necks till when you have killed and wounded many of them, then bind a bond firmly (on them, i.e. take them as captives)… If it had been Allah's Will, He Himself could certainly have punished them (without you). But (He lets you fight), in order to test you, some with others. But those who are killed in the Way of Allah, He will never let their deeds be lost." Holy war is to be pursued against those who reject Allah. The unbelievers are to be killed and wounded. Survivors are to be held captive for ransom. The only reason Allah doesn't do the dirty work himself is to to test the faithfulness of Muslims. Those who kill pass the test. (See also: 47:4 for more context)