First was Dragon Ball Z. As far as I can remember is when my dad was on the sofa watching the Original Japanese Dub whilst I was sitting on his lap watching with him. I was only 1 and a half at the time.
Tough question. The first anime I ever watched I think would be Montana Jones, though I was too young to know what anime was at the time. And then came Pokemon and Digimon and those kind of shows and I began to understand what anime was.