Was admittedly up against a tough field, but it's a movie that's stood the test of time, and absolutely deserved a nomination.
The Dark Knight (2008)
Didn't score a nomination in the very last year there were only 5 Best Picture nominations, and the Academy apparently wasn't risking giving a nod to a genre film.
Singin' in the Rain (1952)
Hands down one of the greatest movie musicals ever, this absolute timeless classic didn't even get nominated, while the winner - "The Greatest Show on Earth" - is probably on no one's "Best movie ever" list.
Eternal Sunshine of the Spotless Mind (2004)
Maybe its art house indie vibe turned off Academy voters, but ten years later, audiences everywhere still appreciate "Eternal Sunshine"
King Kong (1933)
It was the early days of the Academy, but King Kong's impact has endured to this day.
And then a trio of overlooked Hitchcock films:
North By Northwest (1956), Psycho (1957) Vertigo (1958)
What have you got against Hitchcock, Academy?!
2001: A Space Odyssey (1968):
One of the most groundbreaking works of direction, visual storytelling, and all-around spectacle wasn't even nominated in the Best Picture category. (Though Stanley Kubrick was nominated for Best Director and Screenplay, and won Visual Effects)
Do The Right Thing (1989)
One of Spike Lee's first great films isn't even nominated in the year Driving Miss Daisy won.