I don't know about Kilmer. I just watched the documentary about him and he seemed a lot nicer and more professional than his "bad boy" reputation made him out to be.
I read stories about Faye Dunaway being extremely difficult on set and was a diva... allegedly. There are stories out here in the internet about her behavior.
I know that the late Patty Duke and Sean Young both had reputations, but in both cases I think there were mental/health issues involved. The TV actors Katherine Heigl and David Caruso both sidetracked good careers by acting the diva.
Some I expected
Bruce Willis, Marlon Brando, Val Kilmer, Alec Baldwin, Edward Norton.
Not Expected
Julia Roberts, Jennifer Aniston, Sharon Stone...
And others