I've only watched small bits of Higurashi, and it was such a tear-jerker when Rika was stabbing herself to death...
FullMetal Alchemist was such a close tear-jerker when I watched some of the anime, but mostly the manga (I prefer the manga over the anime, in my opinion.), especially when Hughes, Tucker, and Nina died (I was sobbing at, like, 4 or 5 in the morning when I was reading my dad's copies of the manga :'C)
Clannad was quite sad as well (and After Story)...I will admit.
I finally finished watching Soul Eater a few days ago, and it's a GREAT, no, INCREDIBLY AMAZING anime, except when Crona was impailed and (almost) died, I was sobbing like a little child, especially when he/she said "I'm happy now, because you were my friend." to Maka. Makes me shed tears every time. TT__TT