I started watching anime in my teens when the only anime you could readily get in America was Akira, 3x3 eyes, Yamato, Battle of the Planets(Gatchamen), Tokyo Megopolis, or Urotsukidoji. Now there is such a mass amount of anime being produced you can run a whole gamot of tastes and extremes.
I can go for just about anything if it strikes my interestst:
I like Death Note, Hellsing, Cowboy BeeBop, Blood, Vampire Hunter D, and Robotech. Robotech is one of my first animes, nothing like I had ever seen. music, robots, heroes, damsels, enemies and world shaking battles. I'm also into things of a more paranormal subject like D.Greyman, Ghost hunt, Red Garden & Hell Girl.
I am a huge Miyazaki fan, It's my absolute pleasure to watch Totoro, Mononokee, Nausica, Spirited Away and Even Ponyo. I found him because Disney did Atlantis, which is based on a Miyazaki plot outline that became the series "Nadia: Legend of the Blue Waters".
Yeah, I love girl shows... Sailor moon in Japanese with all the implied relations between girls, guys, and inbetween. Transformations, love and romance and cute and funny. Tokyo Mew Mew, Love Hina, Chobits and Strike Witches.
Sometimes I go for Fluffy yaoi like Gakuen Heaven, Ouran High, Junjou Romantica. Shows that are all boys love. Which is not too sexual, but there are alot of overtones of male romance as seen through a girls eyes.
There are a few kiddie shows like Ojamajo Doremi, Pretty Cure and Shugo Chara. Anything real cute, usually involving transformation and lite battles with some comedy.
Then sometimes I like straight Hentai like Bible Black, Kite, la Blue Girl, Demon Hunter Koji, Wet Summer Dreams, or Nymphs of the Statosphere. I even like some ecchi types like Rosario + Vampire, and other panty showing shows.
Not that I don't like more heavy Yaoi titles like: Level C, Fake, My Sexual Harassment, bronze, Ai no Kusabi, Legend of the Blue Wolves.
I will not go without Robotech, Vampire Hunter D, Studio Ghibli(all), Urotsukidoji & Sailor Moon. Eclectic enough for you?