Unlike Catholicism, Islam does not require the mediation of a priest for prayer and worship, but that doesn't mean the Islamic faith lacks clergy. On the contrary, several Islamic figures perform functions similar to that of priests by helping followers better understand their religion and acting as spiritual guides.
Mullah
The term mullah -- often translated as cleric or lord -- denotes several forms of leadership in the Islamic faith. These leaders include kings and other monarchs, but the term mullah most commonly refers to religious leaders and teachers. Much like priests who study the Bible, mullahs study the Quran and help interpret its contents for the laity. They may lead congregants in prayer or recite the Quran during holy periods such as Ramadan, and they typically have some formal religious education.
Imam
The use of the term imam is one of the reasons for the split between Sunnite and Shiite Muslims. Sunnites applied the term to the fallible but morally outstanding religious leaders who succeeded Muhammad, while Shiites argued that an imam was infallible and had special religious insight and divine ordinance from the Islamic God, Allah. Subsequently, Sunnite imams became Islamic religious leaders who lead mosques in prayer much like priests leads churches.
Sheik
Arabic Muslims refer to venerable men older than 50 as sheiks, but this term is flexible and also refers to individuals who have memorized the entirety of the Quran. In both cases, the term sheik has religious connotations, and like priests, sheiks are often theologians who study and interpret holy scripture. They may also act as heads of religious communities, universities or villages.
Ulama
Ulama are Islamic scholars who understand both the practical and theological teachings of Islam. Like a priest, an ulama serves as a religious teacher, though he doesn't necessarily perform religious functions in a mosque. Ulama apply Islamic scripture to everyday problems and often work as lawyers, judges or professors in Islamic polities. Historically, ulama were powerful figures in states like the Ottoman Empire, but in modern times, the power of the ulama class has waned.