Just to correct one of the posters above - the difference between Shias and Sunni may seem political in origins, but is as much doctorinal. One of the most important difference is the shiite belief in continuation of 'ijtehad', which allows interpretation and re-interpretation of religious law in modern times. The Sunnis too allowed this initially, but sometime during the Abbasid reign, and inspired by the skeptics such as Imam Ghazali - they closed the doors of rational interpretation.

Another doctrinal difference is the shiite belief in the institution of Imamate - the belief that the Imams were the rightly chosen successors and infalliables. Sunnis have similar reverence for the companions of the Prophet, but they don't consider them Infalliable.So unlike what one ignorant poster has said above - shias believe in following the teachings of Quran as well as the actions of the Prophet (and the Imams), unlike Sunnis - The second Caliph is said to have proclaimed that Quran was sufficient and he needed no other guidance.

Also - a very recent phenomenon is Wahabism. Wahabis consider themselves an offshoot of Sunni Islam, started merely 200 years back and all terrorist activities can be traced back to this virulent sect. So you would never find a shia or sunni engaging in terrorism, but wahabis (also known by some other names such as Ahle-Hadiths and Salafis)