The Collaborative International Dictionary of English v.0.48:

Sheik \Sheik\, n. [Ar. sheikh, shaykh, a venerable old man, a
   chief, fr. sh[=a]kha to grow or be old.]
   The head of an Arab family, or of a clan or a tribe; also,
   the chief magistrate of an Arab village. The name is also
   applied to Mohammedan ecclesiastics of a high grade. [Written
   also scheik, shaik, sheikh.]
   [1913 Webster] Sheil

WordNet (r) 3.0 (2006):

sheikh
    n 1: the leader of an Arab village or family [syn: sheik,
         tribal sheik, sheikh, tribal sheikh, Arab chief]

Moby Thesaurus II by Grady Ward, 1.0:

52 Moby Thesaurus words for "sheikh":
   Dalai Lama, Holy Roman Emperor, Inca, Kaiser, Muslim rulers, Prinz,
   abdal, ardri, atheling, bey, cacique, caesar, cham, crown prince,
   czar, dervish, emir, fakir, hajji, heir apparent, heir presumptive,
   imam, kaid, khan, king, knez, mikado, mirza, muezzin, mufti,
   mullah, murshid, negus, padishah, pendragon, pharaoh, prince,
   prince consort, prince regent, princeling, princes of India, qadi,
   rig, sachem, sagamore, santon, shah, shahzada, sherif, shogun,
   tenno, tycoon