Manga that changed me:... the When they Cry series, it taught me that you can't defy fate by yourself, but no one can help you unless you let them. It also reaffirmed that sometimes truth isn't the most important thing and that having it and being alone isn't really living. Living happily despite sadness is more important than the truth. I know it seems rather common sense but the way it was presented made you think of that and feel it really strongly.
Puella Magi Madoka Magica is another one. Say what you like about cutesy shows like that, the fact that it's okay to have hope is wonderful. Hope does lead to despair but despair leads to hope as well. It's good to remind people of that.
Um...Digimon. Then again that's the nostalgia in me and that's because they remind you that before you love someone, you need to become friends with them and that even the most evil people deserve a second chance. (except with what happened in Hunters but I get the suspicion Toei is getting letters and that will get fixed. Hopefully.)
Um... I'm also gonna say... on a happier anime, Love So Life, technically a manga but I'm waiting for the fluffy animation. It's a really sweet, earnest manga that helps make some kids happy and shows that everyone isn't completely over their pasts... and it's not a big deal that they aren't and that you aren't supposed to completely move away from your past, but live with it.