I cry at the drop of a hat these days.
First, the ones others have mentioned:
- Clannad -- but only the first season
- Gurren Lagann -- but not the dramatic moment in the first season that's supposed to have that impact
- Kiki's Delivery Service -- everyone is so nice (╥﹏╥)
- Trigun (original) -- Hallelujah
As for my own:
- Haibane Renmei -- everyone is so nice ( ˃̣̣̥⌓˂̣̣̥)
- WorldEnd (AKA SukaSuka AKA What Are You Doing at the End of the World? Are You Busy? Will You Save Us?) -- a tragic romance but it still got to me as it was meant to
- Cowboy Bebop -- the ending of Ed & Faye's stories always get me bawling
- Millennium Actress -- just destroys me more than any other of Kon's works
- The Light of a Firefly Forest
EDIT: I was trying to ignore movies but how could I forget to mention Koe No Katachi (AKA A Slient Voice)? I watch that one every year or two when I need a good cry to kinda reset.