This entry will be about my favorite anime!
Some Classic Shoujo - Sailor Moon is a favorite of mine (if any shoujo fan says they didn't like it, they're lying); Card Captor Sakura (Oh Tomoe, your unrequited love with Sakura is so cute!); Magic Knight Rayearth (I've never seen the whole thing, but I just ordered the whole series woohoo!)
Revolutionary Girl Utena - My favorite anime ever! Roses and honor and duels and girls fighting - how can yo go wrong? It's about this girl (Utena) who finds herself in the middle of a dueling game to win possession of - a girl, Anthy! Utena protects her and more drama unfolds! I like Anthy because I think she's a lot smarter than one would think.
Ikkitousen - So not shoujo. Ok, it's a little ecchi, but I really like this show! Minus the exploding shirts and panty flashes, there's a really good story. It's a fighting anime set in modern day japan, where schools have politics which rule the region. Students advertise themselves as fighters with a magatama stone earring (it looks like half of a ying-yang) it's based on the 12 kingdoms stories - fighters challenge each other with the power of a previous life. I like it because girls fight (and win!) and not to save the world or their boyfriends.
Escaflowne - Classic! My second real anime ever. I started watching it right before Gundam Wing came out on toonami. It features Hitomi, a girl with fortune telling ability. Hitomi gets channeled to a different world called Gaia, where they refer to earth as The Mystic Moon. There's fantasy, sci-fi, some mechs (woot for steampunk Mechs!) and even a little romance.
The Melancholy of Haruhi Suzumiya - I. Am. Haruhi. I run around looking for people to join my club. I convince other members to do activities. I get bored easily, And I am some sort of god. Ok, not the last part. This show is told from the male lead's perspective, Kyon. We watch all of Haruhi's antics from the outside! Also in the show is some sci-fi stuff, but don't tell Haruhi.
Others I love:
My-HiME - Girls with magical skills and weapons fighting evil! Lots of drama! I love it. It has a sequel, My Otome, but I don't like it as much.
Maria Watches Over Us - Schoogirls and beauty and student council and roses! But no magic or dueling this time, just school drama.
Pokemon - ... don't ask.