#1 is Marlon Brando in Last Tango in Paris. No other actor has bared their soul or gone deeper than Brando did for this role. He said that this experience was so traumatizing he would never go that far again for a film. There's a monologue he has while sitting next to his wife's body (she has commited suicide before the film begins) that is so real it is painful to watch. No one, I repeat NO ONE, will ever approach this level of film acting with the natural gifts that Brando possessed.
After that, it's a bit hazy. My favorite female performance is Juliette Binoche in Three Colors: Blue. I've seen interviews with her, and for some reason, she is able to turn her emotions on and off like a faucet. She's a raw nerve in this film, and watching her progress from tragedy to the "liberty" that is the underlying theme of the film is magical.
Also up there is Cate Blanchett in Heaven, which was co-written by Krystof Kieslowski, who was the guy behind the above film. Yeah, she shaved her head for this film, but there's more than that. There is a scene where she learns what really happened when a bomb went off, and I defy anyone to point out better acting than what Blanchett does here. A fearless performance. Seek this out if you haven't seen it.
The remainer of my top 5 consists of Daniel Day-Lewis in Gangs, and probably De Niro in Raging Bull. I don't think there's much I need to say about the former save for the fact that while he's playing a totally iconic, over-the-top character, he never fails to make Bill the Butcher totally human and believable. Look at the little expressions, the gestures. This is NOT a caricature. It's a rare gift to be broad and minimal at the same time.
De Niro, hard to summarize this one. It's not difficult to play someone who's totally unlikeable. But to make him this fascinating, this original...that comes along once in a blue moon. There are so many times in Raging Bull that you want to look away because what is on the screen is something you just don't want to be witness to. That De Niro was willing to go there with Scorsese and give himself over completely to the material is a rarity. Forget the extreme weight gain; the guy who was training De Niro for the boxing scenes said that had he fought competitively he probably would have been a legitimate and well-ranked professional fighter. Wow.