I have to raise my hand for Fruits Basket as well. Wolf's Rain was a close one but I was too confused at the time, and not really sure I was actually watching the end of the series. This is going a while back, but I'm also pretty sure I was misty-eyed at the end of Hana Yori Dango. And Fushigi Yuugi. Yeah, I cried a lot toward the end of that one.
Hm... there might be more, but it all starts to blend together after a while.