The 2011 Oscars has one of the greatest Best Picture nominees of all time. They actually used all 10 slots and only one of them - Toy Story 3 was truly terrible. That being said, they gave it to The King's Speech when there were about 6 other films I liked better. My favorite of that bunch is Inception. I so wish this would've won Best Picture.
2) Sunset Boulevard
It lost to All About Eve, which is also a great movie but Sunset was just so much better. I wish this had won.
3) The Descendants
This one is less about a great movie snubbed and more about me still being annoyed to this day that The Artist was named Best Picture. I'm a sucker for all things tap dance and I still hated that movie. The Descendants for me was the best film nominated that year.