Lilya 4 ever is very touching. But I actually crave that kind of emotional response from films, so there's no way I'm less likely to watch it again.
I can't think of other films either, but sometimes I change the tv channel from violent scenes and realistic horror films. Pointless anger induction, no fun.
I guess I'd need a good reason to watch Requiem for a Dream again, just because I got pissed of by it. I mean, come on, the story is intentionally fucked up to try fucking us up. And it messed with me in the wrong way, if I get too angry at the plot I think it's manipulative then I lose the connection to the characters. What kind of junkie shoots drugs into a gangrened area?
Maybe I was just in the wrong mood. Technically it's a very well made film though.