I don't know whether this limits me to "Best Picture" winners, or if all those movies that won another type of Oscar are also eligible.
If we go with Best Picture, then (only in chronological order, because I really can't compare light musicals to bloody tragedies)
My Fair Lady
Out of Africa
Silence of the Lambs
The English Patient
Shakespeare in Love
Return of the King
I'm not going to bother scanning the list of every movie that's ever won any Oscar, but I'll just throw in
A River Runs Through It
Wallace & Gromit: The Curse of the Were-Rabbit
And yes... my primary loves are musicals, animated children's movies, and bloody shoot-'em-ups.