Like most people, I remember watching a handful of anime on TV as a child without knowing it was "anime" (Pokémon, Yu-Gi-Oh!, Digimon, Dragon Ball Z, etc). I later found out about Toonami and watched plenty of shows there; Inuyasha, YuYu Hakusho, Cowboy Bebop, Naruto, and so on. I'm sure there are others that I'm forgetting, but Inuyasha is easily the one that had the biggest impact on me as a kid, but I still didn't distinguish it as anime at the time.
However, I recently got much more interested in anime (back in Oct-Nov, I believe) after watching Angel Beats!, so I guess you can say that that was the one to do it for me.