I know these have already been suggested but I just wanted to say that I'm totally addicted to Death Note, Fruits Basket and Ouran High School Host Club.
Fruits Basket is the first manga I ever got hooked on. It's a seriously cute school romance/fantasy but sadly the anime only shows about half the series.
Death Note is my absolute favourite because of the realistic art and amazing plot which proves that anime isn't just for kids.
I think this pic basically sums up why I like Ouran High School Host Club pretty well.
(...too many pictures?)