The Sunnis and the Shi'ites compose the two main branches of Islam, similiar to the way Christianity has two main branches (Catholicism and Protestantism).
Shi'ites believe that Islam should be led by descendants of Muhammad, while Sunnis believe that the leader of Islam should be appointed by election and consensus.
Sunnis make up 84 to 90 percent of the world's Muslims. The word Sunni refers to the words and actions of Muhammad. The Sunnis try to follow Muhammad's example of how to live as a Muslim.
After Muhammad's death, some Muslims began to believe that his daughter Fatima and — more importantly — Fatima's husband, 'Ali, were the best sources of the Koran and Islam. Therefore, Fatima and 'Ali should have succeeded Muhammad. The term Shi'a refers to the party of 'Ali, and Shi'ites believe that religious and political leadership of Islamic communities should emulate 'Ali and Fatima.
Sunnis and Shi'ites have strong disagreements. Some Shi'ite rituals are highly offensive to Sunnis, and Shi'ites often fear that Sunnis will eventually require them to follow Sunni law. The violence in Iraq since Saddam Hussein's overthrow is a prime example of this tension. Even though Sunni Islam makes up an overwhelming majority of the world's Muslims, in Iraq, the Shi`ites are the majority, but Saddam Hussein was a Sunni and when he was in power, the Sunnis ruled. Now with a democracy in place in Iraq, the Shi'ites have much more political clout than Sunnis, and fear is making the Sunnis retaliate.
Sufis are another large group of Muslims. Sufism is not a sect like Sunni or Shi'ite, but rather it's Islamic mysticism. So, a Sufi is also either a Sunni or a Shi'ite. There are many orders of Sufism, just like there are many monastic orders in Roman Catholicism.