You guys have a good list. Even though I get hit hard in the feels by some series, I don't think I've cried in many.

1. I cried the first two or three times I watched Pokemon the First Movie.

2. I always tear up on a certain scene in Hikaru no Go (towards the end).

3. One Piece gets a couple sniffles from me. (There are some pretty moving scenes.)

I only watch anime for the laughs or action but these anime caught me off guard..
Flanders no Inu
Your Name
One Piece

Your Name was recommended to me by some of my friends. I was told it was touching and yeah, it is.

Some other touching anime that my friend introduced but I haven't watch:
Clannad
Angel Beats
Anohana

Air TV, Penguin Drum, and Scrapped Princess.

I bawled my eyes out at the end of Assassination Classroom. Such a good ending but so, so sad.

In fact that Assassination Classroom memory is so strong that I'm having trouble remembering what else I've cried during, even though I know it's a lot LOL

I remember crying during Darker Than Black, mostly around Yin's arc.

Also Shouwa Genroku Rakugo Shinjuu, another one that was sad but so, so good.

I really surprised myself by not crying during Ano Hana/The Flower That We Saw That Day. I'm a huge cry baby and it had all the right elements to make me bawl, but for some reason it just didn't quite hit the way other series have.