Raging Bull - Incredible acting, directing, script, editing (which I don't normally even notice), and story. it's about the boxer Jake LaMotta and his problems he had. Very highly recommended.
http://www.youtube.com/watch?v=YiVOwxsa4OM
Pulp Fiction - It's such a crazy movie, the script is so unique. If you saw it when it came out in 94 you'd see how it influenced the next 10 years of movies.
http://www.youtube.com/watch?v=wZBfmBvvotE
No Country For Old Men - it's probably one of the best "find the killer" movies I've ever seen. Very creepy and suspenseful
http://www.youtube.com/watch?v=YBqmKSAHc6w
Magnolia - it's one of those movies where theres multiple story lines (which Pulp Fiction made famous) but theres about 10 story lines and for the first time I've seen, they don't all come together.
http://www.youtube.com/watch?v=zwXDHSrNFbQ
The Departed - from the same director of Raging Bull, it's also a great movie. The story is so interesting and funny at the same time. Based off a Chinese movie called Internal Affairs.
http://www.youtube.com/watch?v=SGWvwjZ0eDc
Pulp Fiction and Magnolia trailers don't do the movie justice, they make them look bad.