Blasphemy!!
I hope you realize you have commited the cardinal sin...ANIME IS NOT CARTOONS!!!

Some of the shows have very adult and/or classical themes, like honor, revenge, sacrifice, etc.
A lot of anime has characters with a "take care of yourself, no whining" attitude, which I love.
And a lot of the time, they are just plain funny and entertaining.
If you like computers/technology and such, I would recommend Ghost in the Shell. Full Metal Alchemist is pretty sweet too.
I would stay away from Bleach at first, just because it is so damn long.

Anyway, hope this was helpful.