Dancer in the Dark (thanks for reminding me about it), Once Were Warriors, Titanic, a whole heap of others but the one I thought of as soon as I saw this question was United 93 I saw it at the cinemas before a choir rehearsal, I thought about it all through choir and then on the train home, 3 and half hours after watching it, I burst into tears. I got some really strange looks and someone asked me if I was OK.
Also a couple of older movies Morning Departure and A Night to Remember.