To begin with, when I watched my first anime, I was not even aware that such a thing like anime existed. I was way too young, perhaps 4 or 5 years old. I think that the first one of all was Astro Boy, but I'm not sure if perhaps before or after that I watched..... shi7, forgot the name, would be something like Captain **** ah, the one of a ninja-like guy, he was always in his motorcycle and stuff, and had a half moon in his forehead, but hell, that was more than 14 years ago so it's very hard to remember. But indeed those 2 were the first I saw. Then it would have been transformers which I know I watched like when I was 7 or 8 years old. Then, like 2 years after, I saw Captain Tsubasa, yet, I still wasn't aware that it was anime. Later on, and then the very first one I became aware it was anime, was Saint Seiya. Ladies and gentlemen, that anime is one of the best series ever made. And then came Dragon Ball and Dragon Ball Z, about a year after that.
But hell, the question was only about the very first one
I think it was Astro Boy after all.