Quentin Tarantino
Stephen Frears
Alan J. Pakula
The Wachowski Brothers (or did they just write the movies?)
Stanley Kubrick
Darren Aronofsky- Pi, Requiem for a Dream
They directed the Matrix films as well.
Nope. 
If I was in a room with Bay, Bruckheimer, and a gun with one bullet, I don’t know what I’d do.
Sam Mendes (American Beauty, Road to Perdition) is rapidly becoming a favorite, as is Bryan Singer (The Usual Suspects, X Men, X2). Neil Jordan, as mentioned, and Curtis Hanson would be on my list as well.