I'd vote for Analyze This too, because the ones in the poll are too alike. I could never choose between Casino and Goodfellas... I did now, but if Analyze This was there, it would get my vote.

I chose Casino because of the glamourous setting (Las Vegas and all) I liked that.

By the way, what I remember most of both movies is how Joe Pesci's character is killed and knowing it a few moments before he goes. In Goodfellas he says "Oh Shit" or something which is absolutely fantastic, but the way he has to dig his own grave just thrilled me a bit more.