I was born into a family of anime addicts. My parents had anime on the TV almost constantly, though the series that I remember best as my first is Sailor Moon. I wasn't crazy about it, until I found out my cousin Cassie liked it. I became a fanatic after that, even dressing up as Usagi, or Serena, as I knew her then, for Halloween, though my dad told me I was more like Amy/Ami.
Other series' that may be counted as my firsts are Dragon Ball, Gundam, though I don't remember which series, Cardcaptor Sakura, Digimon, Pokemon, and Inuyasha. Wow.