John Williams - the justified legend among composers. Remarkable scores. Various classics like Indiana Jones, Harry Potter, Jaws etc. speak for themselves.
Joe Hisaishi - My all time favourite. His scores in Miyazakis films were instrumental in constructing those beautiful films. Unforgettable tracks, an extremely emotional composer.
Clint Mansell - Brilliant too. It's always somehow funny to hear his composition "Lux Aeterna" from Requiem for a Dream used in who knows where...
I'll also mention John Barry, Wojciech Kilar, Ennio Morricone and Bernard Herrman.