I’m sure there have been others, but off the top of my head the most memorable was Mr. Tom Hanks’Philadelphia, throw in Denzel, Antonio and the era, and I was thunderstruck at the time, empowered, even, to make some personal changes in my life.
Waking Life really got me thinking about what happens after death. I’m an atheist, but some of the theories in there about dreams and brain functioning were really fascinating and worth a look.
Hotel Rwanda - I literally just didn’t speak for a while after that movie - just a feeling of complete powerless rage and sadness
In America - what a beautiful, moving film - I watched it alone and then recommended it to everyone I could think of, one I stopped crying. If you haven’t seen it I recommend it heartily!
** Schindler’s List** - It was a time in history I was not privy to, the film really moved me
and, I know this will not be a popular choice but…
Titanic - Until then, the Titanic had seemed so distant (yeah, it was big, I guess), the movie really showed me the size and scope of it
Primer, the movie about the high-tech start-up guys working out of their garage who stumble onto a way to travel back in time. The tone of the film is so…credible, I suppose…that it makes me stop and think about what it means for a film to establish internal consistency and also to mess with it.
I know the OP is mostly about films that change your way of thinking about the topic the film represents - and Primer does that, too - but it is such a well-made movie (for $7000!) that it affects how I think about movies, too.
Crash - I really began opening my eyes more to ways that I may be racist - I know other Canadians that hold themselves in pretty high esteem because they don’t consider themselves racist against black people, but then turn around and make some pretty nasty comments about aboriginal people.