ghost in the shell nuff said
This. (Because you totally couldn't tell that I fangirl all over the Major...) Amazingly insightful, well-written and witty anime, with a stronger female protagonist who is conveniently also very attractive as well as badass. It's thought-provoking too, because it raises some valid philosophical questions. I like Gurren Lagann and Ouran High School Host Club and other more light-hearted shows, but Ghost in the Shell really is awesome. Neon Genesis Evangelion and Bokura Ga Ita are pretty good too. Maybe because I just sit there and cry during every episode...
-different
-better than matrix, inception...etc
-epitomizes the idea of 'the ghost in the machine' (for those who don't realize the resemblance)
-philosophical
-presents a different angle on life
there is so much i can write about this but after you get sick of shounen anime, be sure to watch GITS
If you enjoy Death Note, I recommend you watch Code Geass, Monster (psychological thriller - on par with GITS), Darker than Black, Serial Experiments Lain and Black Lagoon.
many more, pm me if you want to know