Well, the first anime thing I ever saw was Porco Rosso (that Ghibli movie about the fighter pilot who turned into a pig). But the very first anime series I saw was Bleach... not the best show but I'll always love it :3
Why yes, Robotech here too...
It was a long time ago, have it on VHS still somewhere.
Than had a pause for, let's say, 20 years,
and just recently got hook back up to anime with:
My Neighbor Totoro and Chobits.
Now I need to: "Watch all anime!"
I think mine was Pokemon, followed by dragonball Z and shaman king. But that was before I had the internet at my disposal (UK tv needs much more anime imo)