The Kurds in their north of the country and the Shia Muslims in the south are both partly protected by the US-British enforced "no-fly" zones. 

The Kurds have at times opposed the regime and suffered brutal repression in return. Saddam Hussein used chemical weapons against them when they increased opposition activites during the Iran-Iraq war. 
The two main Kurdish parties have a total of about 40,000 armed forces. 

In the south, Shia Muslims have opposed the regime since the early 1980s, when they were backed by Iran during the Iran-Iraq war. According to some reports, the main militant group has a guerrilla force of between 7,000 and 15,000 men.