Ikiru, Tokyo Story, The Diving Bell and the Butterfly, Goodbye Solo. Not sure how well those apply to your criteria--it's been a while since I last saw them. I would search through South Korean, Japanese, and European cinema because they're more likely to have what you're looking for.

Edit: Wow, I completely forgot about Ingmar Bergman. His movies are exactly what you're looking for. The Seventh Seal and Wild Strawberries are classics.