Interesting thread. As for emotional impact, the movie that really gets to me is one that few people have seen -"Dancer in the Dark" (Bjork was the lead character). I never cry in movies, and this one has me bawling every time I see it.
Also, when I was a child, "To Kill a Mockingbird" really affected me.
Have to agree with everyone about American History X and Shawshank Redemption.
I can't believe no one has mentioned that deep-thinking film "Dude, Where's My Car?" (kidding!)