I think I was three or four when I watched Totoro. I really liked it, and I moved onto Pokemon, Speed Racer, Sailor Moon, and then to Digimon, Cardcaptors, Dragonball Z, Yu-gi-oh, then .hack//SIGN, Inu-Yasha, Fruits Basket, Azumanga Daioh, etc.
I think Inu-Yasha or .hack//SIGN was the first time though, that I actually noticed that I liked anime. Or rather, it was the time where I finally said, "I'm an anime fan."