I shed tears of boredom while enduring Twilight. Does that count?
And, hm, I guess I definitely recall shedding a few tears at the end of Titanic. I don't entirely know why, looking back, and I'm not sure why I even admitted to that one, but yeah. Other than that, it's hard to remember, and it's rare I'll actually physically cry at movies, because I just don't really cry all that much, anyway. I'm not saying I'm not affected by films, but that they affect me in a different way than me actually shedding tears. The impact is usually much deeper. Films that did this recently include: Bullhead, The Place Beyond The Pines and Filth, to name a few.
And, although this is a topic about movies, I also shed a tear when (Breaking Bad spoiler ahead - just in case) :