The title pretty much says it all. My nominees:
Harriett Andersson - Through a Glass Darkly
Jack Nicholson - The Shining
Max von Sydow - Hour of the Wolf
Catherine Deneuve - Repulsion
Glenn Close - Fatal Attraction
List your favorites!
Richard E. Grant - How to Get Ahead in Advertising
Nick Nolte in “Affliction”. This movie also features one of the best lines in cinematic history, delivered by a powerful James Coburn. If you’ve seen it, you know what I’m talkin’ about! 
I was going to include Christian Bale in American Psycho as well, but I think he was psycho from the beginning…well, actually, if I exclude on that basis then that would leave only Nicholson. Nevermind. OK, maybe I amend this to be “best depictions of psychosis in film” then.
The mother in Donnie Darko has an excellently understated mental breakdown at the end. (Well, it’s not a collapse, but at least borderline)
My favourite is probably the mother in American Beauty, if that qualifies.
Humphey Bogart’s testimony in The Caine Mutiny
At the end of her first guest run on E.R., Sally Field acted out a rather impressive breakdown. I can’t find the specific clip at the moment, but here’s a related one.
Bruce Willis in Twelve Monkeys, though he may not be totally stable to begin with.
Sally Field - Sybil, and the funeral scene in Steel Magnolias
Sean Penn - Hurlyburly
Timothy Hutton - Ordinary People
Ellen Burstyn - Requiem for a Dream
Ally Sheedy - High Art
Russell Crowe - Beautiful Mind
Christopher Walken - Deer Hunter
Jessica Lange - Frances
Jennifer Jason Leigh - Single White Female and Mrs. Parker
Gary Oldman and Chloe Webb - Sid and Nancy
Ooh, that is a good one - especially as you’re never actually sure whether his delusions are real.
I’ll add Michael Douglas in Falling Down.
Bob Geldof in Pink Floyd’s The Wall deserves a mention too, I think.
Fredric March as Matthew Harrison Brady in Inherit the Wind.
Nicole Kidman - The Hours
Crap, forgot Ed Norton/Brad Pitt in Fight Club
This is whom I came in to mention.
Just a thought, maybe Stallone in First Blood qualifies too…
Oh, come on, who hasn’t wrecked their hotel room, scared the hell out of a groupie, shaved off all their body hair, then gone for a relaxing swim?
Johnny Depp in Secret Window
Steve McQueen in Papillon
I’ve seen pretty much all of the movies mentioned so far, but I still have to nominate Peter Greene in Clean, Shaven over all of them. That movie still haunts me.
Gene Hackman in The Conversation.
The lead character in Eraserhead.
Does Ray Milland in THE LOST WEEKEND count?