Hmm I tend to stay away from a series that I know will be depressing but Eureka 7 was not too bad imo at least they were together.
There are a lot of individual episodes however that have made me teary eyed (I can't say I've cried but instead that burning sensation before the tears start. I have had enough real life drama to shead tears over so it will take a lot for a fictional story to make me cry), like Clannad episode 14 (the breif case part was really a touching moment), and Cowboy Bebop when Spike finaly finds Julia...
Rurouni Kenshin: Tsuiokuhen (Samurai X) was a sad one.
Prism Ark (so much potential and they just speed through 12 eps, half of which seem like fillers
)
Full Metal Alchemist - There are a few really sad episodes, the 2 that come to mind though are :Night of the Chimara's Cry", and the one with Hues...)
Dragonaut episode 16 - You just have to watch it cause I don't want to give away spoilers.
there are some more but like I said for me it's certain episodes more than a series as a whole.