Hmm, I guess pokemon, but I don't want that to count. I didn't even know Pokemon wasn't American when I was a kid.
It was a friend who got me into manga, and I was really into that for a good while before I found out about anime streaming services, even then I stuck with dubs. So the first anime I watched after getting into that stuff was either Chobits, Kill Me Baby or Lucky Star. I don't know which. I have a strong feeling it was Chobits though. Loved that anime, I've been through both the manga and the show multiple times and I binge each time I go through.
I know for a fact that the first anime I watched subbed was Angel Beats. I was always making excuses to not watched subs and I preferred to go with dubs or manga if I couldn't stand the voice acting. This was the first one that I wanted to watch enough that I stopped making excuses. Didn't look back after that, though I do remember it taking a few episodes to get used to reading subs, I was fine and crying like a little kid by the end. Damn that ending is sad.