This question originally appeared on Quora. 
Answer by Mark Hughes, screenwriter and Forbes blogger
In terms of great performances that were nominated but didn't win despite deserving to win, the most recent glaring one that comes to mind is Mickey Rourke in The Wrestler. Instead of Rourke, Sean Penn won for his performance in Milk. While I'm a fan of Penn's and I liked that movie, and I mean no disrespect to Penn's performance, I cannot fathom that Rourke didn't win that Oscar. He gave the performance of a lifetime, easily one of the greatest of the last decade, and they shouldn't even have needed to have a vote, they should've just mailed him the Oscar after the film opened because it was that amazing.
Felicity Huffman definitely should've won for Transamerica, but the Oscar went to Reese Witherspoon for Walk the Line. I can't help feeling that part of the reason for the loss was that not enough AA voters even saw Transamerica, while Witherspoon's role and film were much loved that year.
Another of the most glaring examples of nominees who should've walked away with the Oscar but didn't, is Ed Norton in American History X. The award that year went instead to Roberto Benigini for Life Is Beautiful, but Norton delivered a performance that is among the all-time best, up there with De Niro in Taxi Driver. It was shocking that he didn't receive the award for what was easily the year's very best performance.
Cate Blanchett's Elizabeth was easily the finest performance of its year, but lost to Gwyneth Paltrow's Shakespeare In Love (a film that swept a lot of Oscars, much to my chagrin). Blanchett was sublime, with a grandeur and passion no other performance that year could match. This was just one example of a few in which Blanchett demonstrated an immensity of talent that dwarfed her competitors, and yet she only occasionally won.
I'll name a controversial one next, but I firmly believe it's true. John Travolta should've won for Pulp Fiction, not Tom Hanks for Forest Gump. Travolta's was the more daring, varied role, and I think that decades from now, his lack of a win will be looked back on as one of the examples of Academy mistakes.
Some other nominees who should've won but didn't include Robert De Niro in Taxi Driver, Robert Downey Jr. in Chaplin, and Denzel Washington in Malcolm X. Note that those last two films came out the same year, and either of them would've been a deserved win.