Technically, the first one I ever saw was Sailor Moon for about five minutes before I kind of figured I really wasn't the target audience for that. I found the animation style to be interesting and different from what I was typically used to seeing in American cartoons, but I didn't keep watching it.

Since then, I have seen stuff like Pokemon (obviously), Yu-gi-oh, Death Note, and Bleach. I'm currently trying to decide whether to get into Ghost in in the Shell, Attack on Titan, or Cowboy Bebop. All three of them seem really good and I've heard good things about all of them.