Yemen

The Sa'dah insurgency by Shi'ite rebels against the Sunni government. Qurrently quiet, but simmering.
 
The conflict, beginning in 2004, is between northern Shi’ite rebels of the Zaydi sect, or ‘Young Believers’, supporters of the late Sheikh Hussein al-Houthi, and the Sunni government. Hundreds dead and over 50,000 displaced. This Islamist movement is also anti-American, though not connected with al Qaeda - it is more influenced by the general enmity between minority Shi'ites and Wahhabi Sunnis acros the Arabian peninsula. Resentments are regional, tribal and religious, opposing government centralism and the local influence of USA. They are affected also by plenteous uncontrolled supplies of weaponry and Yemeni jihadis with experience from other conflicts, plus oil deposits in the north. Yemen has also been a base for al Qaeda-related activities. Currently the conflict is restricted to armed incidents, but humanitarian effects are widespread.
 

Links:

New Internationalist country profiles
Int'l Crisis Group: Yemen