I can't really remember that well, since a program on TV used to show anime in the mornings before school when I was around five, and back then I'd watch Naruto, Yu-Gi-Oh!, Tokyo Mew Mew, Pokémon, Digimon - a ton of stuff XD But I think the first anime I ever really got into, as in watching for the express purpose of watching anime for the storyline, etc. would have been either Tokyo Mew Mew or Azumanga Daioh XD