The most notorious is al-Qaeda, responsible for the September 11, 2002 attacks. They have strong links with what was effectively a state terrorist government in Afghanistan, the Taliban, prior to its overthrow in the wake of US military intervention.
al-Qaeda also are strongly linked to Jemaah Islamiyah an Indonesian and Malaysian based organisation dedicated to the establishment of an Islamic state in the region.
Another organisation which has troubled intelligence agencies has been the Aum Shinrikyo cult in Japan. The group were responsible for the sarin nerve gas attacks on the Tokyo subway in 1995 in which 12 people were killed. This organisation has now been disbanded but has subsequently regrouped under a new name, the Aleph[?].
wikipedia.org dumped 2003-03-17 with terodump