Pretty self explanatory. Since there are many genres. I am going to start off basic.
Animation- Spirit Away
Comedy- tied with Dr. Strangelove and Monty Python and the Life of Brian
Drama- The Shawshank Redemption
Superhero- The Dark Knight
Gangster- The Godfather
Documentary- Expelled: No Intelligence Allowed...just kidding! that movie stunk! Man on Wire was really good
Fantasy- Lord of the Rings Triology
Horror/Thriller- Silence of the Lambs
Musical- Sweeney Todd: The Demon Barber of Fleet Street
Romance- It's A Wonderful Life and yes I've always considered that movie a romance
Science Fiction: 2001: A Space Odyssey
Sports: Raging Bull
War: Saving Private Ryan
Western: The Unforgiven