Favorite Movies:

I personally have a soft spot for third world journalism movies:

Under Fire
Live from Baghdad
Salvador
The Year of Living Dangerously
We Were Soldiers...
Ghandi
The Quiet American (Undecided about this one)

Other Old Movies:

Barcelona
The Last Days of Disco
Metropolitan (The above three are Whit Stillman movies, my favorite director)

The Enemy Below
The Battle of New Orleans
Top Gun
An Officer and a Gentleman
Das Boot
Mutiny on the Bounty (the 1935 Clark Gable one)
(Generally a big fan of naval movies)

To Live
Eat Drink Man Woman
Mikan no taikyoku (The Go Masters)
(I like chinese movies)

The Charge of the Light Brigade
Black Hawk Down (war movies)

The Paper Chase
Love Story
With Honors (oddly three Harvard movies)

The Godfather (Only 1 really)
Casablanca
Roman Holiday (also a journalism movie, though set in Italy)

Recent Movies:

Man on the Train
Gods and Generals (which I thought was better than Gettysburg)
Master and Commander (naval movies again)
Mystic River

(I'm not a huge fan of Brendan Frasier despite having two of his movies on the list.)

This is probably an incomplete and idiosyncratic picture of my favorite movies, but the best I can do off the top of my head. I didn't include movies that are really filmed plays. (Though Casablanca was based on an unproduced play.)