Oh my well, aren't we going back a long way now... first anime I suppose was technically a few episodes of Cardcaptor Sakura (or just Cardcaptors as the dub was known) when they were on TV (CITV if memory serves). Then of course there was Pokémon for a while, if that counts, and Shaman King a few years down the line, plus the occasional bit of Yu-Gi-Oh and its various rip-offs, like Duel Masters, all on Fox Kids or Cartoon Network or one of the other kids' channels. But I didn't really make the distinction of them being "anime" rather than just "cartoons" at the time. The first anime I watched as an anime, if you like, was Lucky Star, despite being tempted by various more stereotypically shounen anime before then. I don't even remember why exactly I decided to start watching LS in particular... I recall something about the theme being used on a Dynasty/Samurai Warriors parody (courtesy of Nico Nico Douga no doubt). Loved it. Senogku Basara's anime adaptation sealed the deal. Been watching the stuff ever since (all those weeks ago... hah hah...)
tl;dr: If you're reading this, you don't care.