Not sure if it counts as anime--Voltron: Defender of the Universe was a very popular cartoon when I was a kid, and it fascinated me because it was different from the other cartoons I watched. It was the founding stepping stone toward my interest in anime later in my life. First two full length anime films I ever watched as an adult: Akira then Ghost in the Shell. I tried to like Cowboy Bebop. So very tried, because others raved about it. I was not a cool kid in this, however.
Wow, I completely forgot about Voltron. I spent a lot of time as a kid watching that and Speed Racer, and would like to rescind my statement in this comment with regards to the first anime thing. At some point after those shows was a lot of time spent watching DBZ and Yu-Gi-Oh, neither of which I would consider very good. Guess I've watched more anime than I thought. Loved both of those shows as a kid but wasn't aware of what exactly they were. Mostly the same thing as you, but I haven't progressed very far into anime.