For me it's definitely Blood Diamond, still gets me after having seen it several times. Titanic used to make me cry xD (as some animated movies....

), but also De Tweeling ( a Dutch film), Miss Potter, A Walk to Remember and some I don't recall at the moment.
I can't watch it with other people in the room because I don't want them to see me cry so hard.
I also often try to avoid such circumstances. When it's at my parents' place, it's not really a big deal, because they don't really think it's weird, but when I'm with friends I try to avoid crying at films, which only just worked out when I saw Blood Diamond for the first time. I was sitting ther, tears filling my eyes and I tried to blink them away, which worked good enough at the moment.