Cartoons are not a children's medium. It's as simple as that. I enjoy my occasional cartoon from when I was younger, but I mainly love the more mature animated shows and films, like a lot of anime and the very, very rare work of western animation that actually takes the medium seriously (in other words, Pixar and Avatar: The Last Airbender).
Animation is perfectly capable of telling good and dramatic stories. I can't stand it when people don't understand that ("Wait, Up is really emotional? But isn't it a cartoon?"). It's such a closed-minded and artistically ignorant way of looking at film in general to think that animation is somehow inherently incapable of serious and good storytelling.
As for favorites, Avatar: The Last Airbender is not only my favorite cartoon, it's my favorite show ever. Impressive considering it's technically a kids show and I'm 21, but then most of that show's fanbase is high school and college age...