Here's the list of Best Picture winners and one of the nominations that should have won it. The first movie is the picture that won, the second is the film that should have won. I'll start from the 70s.
The Sting/American Graffiti
Godfather 2/Chinatown
One Flew Over The Cuckoo's Nest/Jaws
Annie Hall/Star Wars
Kramer VS Kramer/Apocalypse Now (although Kramer vs Kramer was an extremely powerful film).
Chariot's of Fire/Raiders of the Lost Ark
Gandhi/ET
Titanic/Good Will Hunting
Shakespeare In Love/Saving Private Ryan
American Beauty/The Green Mile
A Beautiful Mind/Lord of the Rings
The Sting/American Graffiti
Godfather 2/Chinatown
One Flew Over The Cuckoo's Nest/Jaws
Annie Hall/Star Wars
Kramer VS Kramer/Apocalypse Now (although Kramer vs Kramer was an extremely powerful film).
Chariot's of Fire/Raiders of the Lost Ark
Gandhi/ET
Titanic/Good Will Hunting
Shakespeare In Love/Saving Private Ryan
American Beauty/The Green Mile
A Beautiful Mind/Lord of the Rings