Philippines

Ongoing conflict, flaring up and subsiding. A longstanding Muslim-Catholic conflict. 160,000 deaths, 2m displaced.
 
Historic background: the Spanish invasion in the 1500s, merging widely different island cultures under one foreign Catholic jurisdiction. Several conflicts are involved, the main one being the longterm Moro rebellion in the mainly-Muslim Sulu archipelago against Catholic and American dominance. Mindanao is the main island of Sulu.
 
The 1970s spawned several Muslim political movements, the most successful being the Moro National Liberation Front (MNLF), which unified disparate Muslim bands, gaining support from Libya and Malaysia. In 1976, the MNLF (later called MILF) agreed with the Marcos regime to the formation of an autonomous Muslim state ruled by Islamic law, instead of full secession from the Philippines. Talks broke down in 1977 and clashes continued - Marcos encouraged factionalism to divide the movement.
 
In 1989, four provinces were designated autonomous by President Aquino, and things went well until 1989-2001, when outbreaks of violence took place. A popular plebiscite in 2001 voted against expansion of Muslim autonomous areas.
 
Recent outbreaks in 2006-8, not least against government corruption. A Malaysian-brokered agreement was aborted in 2008 when rival Muslim groups disputed the main MILF's right to negotiate and the constitutionality of the agreement for autonomy. Renewed fighting, 600,000 displaced. Government insists on disarmament first, MILF insists on agreement before disarmament. Threats also against MILF from a radical Christian armed group in Mindanao.
 
The Muslims in Mindanao are still divided, sporadically clashing with government troops. The government seeks mainly to eliminate al Qa'eda-related forces such as Abu Sayyaf, a radical terror group. General public reconciliation has grown in momentum, and Islam has increasingly been accepted as part of Philippine culture, but government and extremists are still in conflict.
 

Links:

Everything: the Moro Rebellion
Wikipedia: the Moro Rebellion
Flashpoints: the Philippines
Reuters Alertnet: Philippines