Angel Beats is incredible, if you haven't watched it you should - it's not very long so it's not like you're making a massive commitment, and it's one of the best animes I've ever seen. <3
I also love a really cute one called Azumanga Daioh about a group of girls in high school in Japan. It's so funny and so cute. Honestly a classic in my opinion - those jokes are gold.
Another one I really like is Case Closed (aka Detective Conan) about a teen detective who is slipped poison, but instead of dying he shrinks to have the body of a child! I've never managed to get that far in (it's so long - I think I got to around episode 100 before getting bored the last time I tried) but it has some really great episodes, and some of the mysteries... I'm in awe. Moonlight Sonata is one that comes to mind - I can't listen to that song without crying anymore! O:
And finally, Shingeki no Kyojin, or Attack on Titan! It's really awesome, but taking a while to come out with series 2... }: