I must say I don't look much anime as before, so my list is kind of old, but here it goes!
I love Full Metal Alchemist.. that anime just brings a lot of feelings to me.
I also love Death Note. It's such a smart anime, when I saw it for first time I couldn't belive all the plot twists and the intelligence of characters
I'm a fan of Tsubasa Chronicles. I just can't stop crying with the serie. It's sad that a lot of people hate it for the draw style. I find it beautiful.
Those are my favorite animes
I have a lot of favorite mangas:
Full moon wo sagashite, Fruit basket (manga not anime!), etc.