Thought of a few more that have not been said.
Dustin Hoffman got robbed for Tootsie. Ben Kingsley did a great job in Ghandi, but comedy is often much more difficult than drama, and the way Hoffman pulled off that role is awe-inspiring. He had two adapt two completely different personas, one a different gender, and he absolutely nailed it.
Heat was massively snubbed back in 1995. It didn't get one nomination. I haven't seen Braveheart, but I highly doubt it's superior to Heat. Heat's cast is impeccable, and Mann is a superior director to Gibson.
JFK should've won over Silence Of The Lambs in 1991. SOTL is an excellent film, but JFK was far more powerful and entertaining. And the lack of Oscar nods for that film's acting is a robbery as well. Tommy Lee Jones was great in int, but Joe Pesci and John Candy would've been more deserving nomnations in that tehy both pulled off roles that public most moviegoer's general perception of them. Costner got snubbed for Best Actor as well.
Bill Murray should've won for Ghostbusters in 1984. Once again, this is a case of the Academy ignoring the merits of comedic acting. Murray's performance in the film is incredible. He absolutely nails the character's persona and his comedic timing and delivering is perfect. Big snub.
Spielberg should've won for Jaws in 1975 isntead of Milos Forman for One Flew Over The Cuckoo's. Cuckoo's Nest is a superior film, but the direction in Jaws is incredible. The way it was actually filmed, especially the shark sequences, are incredible.
Going back into the Academy's long history of robberies, in 1956, Yul Brynner should've scored Best Supporting Actor in The Ten Commandments. He played Ramses to a tee and along with Heston's Moses is probably the best prtrayal of a Biblical figure ever put on screen. Also the film itself should've won for Art Direction and Best Picture.
Delving even further, in 1952, High Noon should've won a victory over The Greatest Show On Earth. But with the exception of Unforgiven, Westerns often get a snub
Alec Baldwin should've at least gotten a nod for Best Supproting Actor in The Departed and Glengarry Glen Ross.