Dramas I have enjoyed:

Shawshank Redemption

Garden State

Crash

Into the Wild

The Social Network

Big Fish

Truman Show

I tried to stick to ones that didn't have action sequences to drive the audience's attention. I'm kind of with Lee on this category, these are the ones I felt emotionally invested in when watching them the first time in the theater. In trying to find similarities, I would probably say great acting performances drove a lot of these to be great movies rather than simply story or film direction. I will forever think Jim Carrey got screwed for not picking up an Oscar nod for Truman Show. I thought it was an ingenious combination of comedy and drama.