One of the first cartoons I remember seeing was technically anime - Kimba the White Lion, which was in an hour block with Speed Racer.
Did not see much more until local channels started "fighting" with it with the kind of mangled but still cool American version of Robotech on one, and Battle of the Planets (aka "Science Ninja Team Gatchaman" and later aka Eagle Riders, G-Force and another I keep forgetting), Voltron (both the GoLion version and the vehicle version in rotation) and a few others that failed to hold my attention as well as Battle, Voltron and Robotech.
Then again, I was also always a big fan of giant monsters (starting with my introduction to Gorgo and moving on to the other two Big G's - Gamera and Godzilla) and discovered Ultraman (aka "Ultraman66") just as I was getting interested in superheroes in general.
One piece. Unless you count pokemon.
At a local convention (Saturday Morning ConToons), there was a seminar on the history of anime. Pokemon and DragonBall Z tie for the "first mainstream anime to have little serious editing in American markets"; first "actual" anime was MegaMan (or maybe it was AstroBoy - get them confused and have seen exactly one episode of each) in the early 60s, followed by Eight Man, Speed Racer, Kimba the White Lion and a few others. The "middle renaissance" of Japanese Animation in the US was the Harmony Gold/Carl Macek version of Robotech in the 80s.
Pokemon even stood out at the time as the first one that had all but two episodes translated as directly as possible - those two were deemed "to idiosyncratically Japanese" and generally can only be found on places like CrunchyRoll or in Japanese collections (one of them focused on a Tea Ceremony and the other was apparently cut up and used as "filler" in later Pokemon series but never aired on its own)