Apart from the usual childhood anime, I think the show that got me into being a rabid fan would be Kanon 2006. I don't remember how I can across it, but it really got me engaged in anime.
Probably either Samurai Pizza Cats, Tekkaman Blade or DBZ. Although at the time I had no idea they were anime, I just thought they were normal cartoons.
Like many others I watched Pokemon, Sailor Moon, Dragon Ball and the sort. Though the first series I went out to watch with subs was the original Full metal alchemist adaptation.
Pokemon for me and I didn't even want to watch it until my parents showed it to me on television and then I got hooked. Afterwards it was stuff on Toonami like Tenchi Muyo, Dragon Ball Z, Big-O, and Yu Yu Hakusho.
I watched some classics like Pokemon and DragonBall when I was a kid, but what hooked me into anime when I was a teen is Death Note. Pretty good series, even after taking off the nostalgia googles.