The four main branches of Islam are Shia, Sunni, Wahhabi and Sufi. There are, however, over 150 different smaller sects of Islam in total, along with the semi-hybrid religion Bahaiism.
The first division in Islam resulted in the Sunni and Shia branches. Sunnis make up between 84 and 90 percent of Muslims and are relatively comfortable following Islam in a secular society. They believe in a caliphate with a leader who is both spiritual and secular head of the Islamic world. The caliph is the rightful heir of Muhammad's place, a designated leader not necessarily related to his predecessor.
Shi'ites make up most of the remaining non-Sunni Muslim world. They split with Sunnis over the fifth caliph. Shi'ites wanted Muhammad's son-in-law Ali to succeed him, and they believed that all caliphs should have belonged to Muhammad's bloodline. The Shia use a different set of holy books from the Sunni.
Wahhabis, Sufis and the Bahai are of much more recent genesis. Wahhabism was founded in the early 1700s in a fundamentalist militant movement led by Abd al-Wahhab. Sufis, who are primarily from Persia, are a mystical branch of Islam heavily influenced by Indian Vedantic philosophy. The Bahai are of Persian origin but moved into India later. Bahaiism was started by Mirza Hussayn Ali in 1847, and its adherents work toward integrating the three great monotheistic religions of the world into one philosophy.