Although I could pick any movie that has made me cry, I would probably have to only pick two films, both of which are directed by Darren Aronofsky:
1.) Requiem for a Dream. The tragedy in this film is almost Shakespearean. Four unlucky souls harnessed by the addictions they have, each of them spiraling down into their own personal hell. I had to cry, mostly due to the strength of it's actors (ESPECIALLY Ellen Burstyn who was fucking robbed of her Oscar award), but mostly because things like that actually happen, and no other movie has ever really had the balls to convey it with such grit and realism to make it emotionally lasting. It's a movie that emotionally affects you, whether you want it to or not.
2.) The Fountain. While Aronofsky's Requiem gave emotions of trauma and a psychological disturbance, The Fountain left emotions of beauty, mostly because of the visual effects. It's one of the rare movies that uses visuals in order to provoke emotion rather than just show off a technological hard-on. Although each scene has a strangely luminescent golden glow, the most spectacular scenes take place in the spaceship which makes its way into a nebula, with golden clouds thundering in the background as our main character bodes tearful farewells to his deceased loved one. It's artsy, definitely, but it just kept me up at night at how god damn beautiful the fucking movie is.
I haven't seen The Wrestler yet (Which was also directed by Aronofsky) but I have a feeling I'll love it as well.