An uncountable number of Animes did. Clannad being probably the first. Full Moon wo Sagashite, AnoHana, AnoNatsu, Onegai series a couple of times if I had to name a few of 'em
5 centimeters per second, Clannad, Angel Beats, Fate/Stay Night, Full Metal Panic (from laughing), Saikano and a whole bunch of others have made me cry at some point. Anime that doesn't thouch you emotionally never become truly great, at least in my opinion.
I watched all of Key works, EF, AnoHana(almost broke a tear) and etc and they got me really sad but the only time i really cried was when the strawhats were burning the Merry in OP. I cried over a boat.
Yu-Gi-Oh!:DM made me cry a little @ the end when Yami Yugi (A.K.A. Atem) lost the duel with little Yugi & he goes back to Egypt the past,also,the other anime endings that made me cry a lot is Sailor Moon,Dragonball GT, & Gundam Wing (EW).
Angel Beats, Gosick, and Chrono Crusade all made me cry at different parts. In the case of Angel Beats and Chrono Crusade, it was because of how sad the ending was. For Gosick, it was both happiness and sadness because of the events of the last episode or two. I'm sure there are others, but those three are definitely tops on the tear list.