I've seen quite a few animes since my last post, so I'll add a few. Though it seems a lot of people have already mentioned these, so it might be redundant. Nevertheless!
Air. Both the series and the movie were flawless works of art in my opinion, and the level of emotional involvement was very high. Misuzu was absolutely adorable (Nihaha), which made the whole anime all the more depressing. I can't help but smile when I think of her,
Hanbun no Tsuki ga Noboru Sora. I'm amazed they managed to put so much emotion, feeling and story into just 6 episodes. The series was less sad than Air, but it was still quitel an emotionally draining experience.