Man this is rough.
I. Lawrence of Arabia
II. A Clockwork Orange
III. Mr. Smith Goes to Washington
IV. The Treasure of the Sierra Madre
V. Midnight Cowboy
VI. Star Wars (the trilogy overall, if not the first one)
VII. Jaws
VIII. Full Metal Jacket
IX. Goodfellas
X. The Social Network
Tried to have some variety here and I've homered on a few I personally like that are probably not as good as some others (mainly The Social Network and Jaws) but God damn do I love those movies.
Others are probably "better", like Apocalypse Now, Citizen Kane, Seven Samurai, The Good, the Bad, and the Ugly, but I feel like the ones above give a pretty good sampler, you got a Western, a war movie, a contemporary movie, 60's, etc.