Sailor Moon and DBZ, but those were the American TV broadcasts, which don't count that much - didn't realize they weren't American as a kid.
First anime I watched that caught my attention on the medium would be the Ghost in the Shell movie. Blew me away. Then I managed to see some 3x3 Eyes OVA combo, then Akira, then finally Cowboy Bebop. At this point I was really curious on the medium. Saw Metropolis before finally watching my first subbed anime, Azumanga Daioh. From there it was off to the races.