Sailor Moon, Utena, Project A-ko, Ghost in the Shell, Gatchaman, Space Battleship Yamato, Strawberry Panic, and more. All Japanese Animation I adore. Some old, some new. Hulu and Netfix have a pretty good selection of anime. I just finished the first season of "Birdy the Mighty: Decode" and I gotta say...I LOVED it.
The story starts with Birdy, our heroine, trying to capture some bad guys in space. She ends up getting assigned to earth because they are hiding out on our planet. She accidentally kills a young human boy. Well, she mangles his body all up. She manages to "save" him by bringing his consciousness or awareness into her body as the people she works for repair his. So it's two people in one body. She continues her search by night because she has to trade out with him during the day so he doesn't flunk out of school.
There's plenty of action, but the characters are awesome. You really do get involved and care. The thing I love best about Japanese Animation is that you really never know who will live or die. Including your main protagonist. I've watched anime before that left me utterly heartbroken, yet completely satisfied. The sacrifice was justified and epic. I have no idea how Birdy will end, but the end of the first season was intense.
So, if you love Anime, check this one out. If you have never seen any Japanese animation, then this is a fun one to start with. It's on Netflix right now. It's dubbed (I like mine subtitled) but the dubbing is excellent. Great voices that match the characters perfectly.