Futurama made me cry a couple of times. Namely the episodes Luck of the Fryish and Jurassic Bark.
Although they are anime I can not leave them out, One Piece and Fullmetal Alchemist have also made me cry. One Piece a whole lot.
Yes to all this (except FMA because I haven't seen much yet). Though I find Jurassic Bark just plain depressing and horrible. Luck of the Fryish I love and will always watch to the end when I see it on because it's happy tears, haha.
Also the one where Leela gets stung by those giant bees and spend most of the episode hallucinating, then at the end you see Fry has been next to her hospital bed the whole time...
In One Piece, Nami's backstory, Robin's backstory and Brook's backstory do it to me. The Luffy/Usopp Water 7 ordeal did it too.
Edit: And the burning of Going Merry killed me. I forgot about it until I read it in here, I think I repressed it because it hurt so much.
On Farscape, when Zhaan dies, and when Talyn-John dies. And then when Talyn and Crais die. (That show is angst central.)
Does reality/documentary TV count? Because almost anything about adoption is liable to bring on happy tears too. I'm not sure why, since I'm not adopted, or anything.
Also, to my eternal shame, I got teary at the end of High School Musical 3. (Shut up! LOL.)