Anime that made me actually cry (most to least from top to bottom)
Angel Beats!: This anime had me crying the most by a long shot. Maybe it's because it hit home with it's ending. I've had to give a lot up in my life that I held very dear so it may have gotten to me more than it would most but none the less, I think there are few people who can say that didn't at least tear up.
Ano Hi Mita Hana: Another real tear jerker and overall one of the most touching anime in existence. This one is much more touching and moving than Angel Beats but didn't hit me as hard. This one is that way consistently throughout the anime unlike Angel Beats but still isn't first place because it doesn't hit you like a ton of bricks quiet the same way.
Katanagatari: I won't say anything regarding why this anime is ranked number three on this list because there isn't anything I can say that won't spoil the ending. Except for this... It's badass as well as tear jerking.
Shiki: I'm not sure if other people found Shiki to be as moving as I did but it really got to me at certain times, especially the last few episodes. I won't say anymore to avoid spoilers...
Clannad: The whole ordeal with the girl and the wood stars had me in tears on several occasions. You won't regret watching this anime.
(This list's tags are those of the anime included in this list and not tagged for the theme of the list itself.)