I love anime that either involves Mechs, a romantic story within a darker one, a complex storyline, or is a pure comedy... That's kind of vague, isn't it?
Well, my favorite are Rozen Maiden, Azumanga and Escaflowne... Hopefully, the gives you an idea of the kind I like...
I don't like it when the anime loses it's plot and goes into loads of fillers, though... That usually puts me off the anime *cough*Naruto*cough*Bleach*cough*