I'm not a Disney fan and although I've watched quite a lot of Cartoon Network's stuff I don't see myself as a fan of it either. I'm more into animu.
My top ten, not in any order:
Ginga Nagareboshi Gin
The story probably everyone knows(?). A little tiger striped akita dog who leaves to a journey with his friends for collecting enough dogs so they could kill a monster bear Akakabuto. GNG was probably my first anime ever, and back then I didn't even know it was anime.
Puella Magi Madoka Magica
One of my newest findings, and it was so exciting I had to watch all of the episodes right away. I love the way it's been drawn and the music is so beautiful it gives me chills. Everyone who hate magical girl shows should watch this since it's about the darker side of being a magical girl.
Vandread
A mecha/scifi show about men and women who've been living on different planets and living in war for a couple of generations. Three men end up into women's pirate spacecraft and they have no choice but to learn to get along with each other. They also find out that men and women have a common enemy they can't beat without combining powers.
Sailor Moon
I've been in love with this show since they started to show it here. Probably one of the most known magical girl shows out there. Monster of the day theme and lots of repeated attacks and transformations but I couldn't care less. I just love the characters and the story so much. The climax episodes are really dramatic.
Digimon Tamers
My favourite season of the Digimon series, probably because it's somewhat darker than the rest of them. And there's less characters so they're easier to emphatize with imo. There's also two of my fav digimons ever: Renamon and Impmon + their evolutions. I also like the musics of DT a lot more than in the other seasons.
Mai HiME
Yet another magical girl series. (I just love these.) This is partly similar with Madoka Magica, but not as dark. However, this too gets quite ugly in the middle of the series. Music gives me eargasms and I love especially much HiME's "children" they command: mecha-like monsters who assist their masters in battles.
Fruits Basket
This is probably one of the cutest series I've seen. It's about an orphan girl who meets a big family with a zodiac curse: every time someone of the opposing gender hugs them they transform into their zodiac animal. Although the show is cute and makes me happy there's some characters whose background stories are really heartbreaking.
Lucky Star
You're not supposed to use your brain while watching this. LS is about cute highschool girls and their everyday life. There's no any dramatic, long plot in this, but I guess the main purpose is just to be fun slice of life show.
Pokémon (Indigo League)
The first season of Pokémon, oh yeah! I became totally hooked in this when I first saw the opening. This was before fans had grown tired of Ash and when he still had the right to be a complete nubcake - and it was fun and entertaining as hell. + all of the nostalgic value.
Elfen Lied
Probably the gloomiest and saddest show I've ever seen, yet I can't help but to like it. I can emphatize with Lucy so much I'm just crying most of the time while watching this.