For me? Well, I've got a few vague memories, but I can't classify which one came first. So I'll just tell all of them. o.o;
First, I remember Hello Kitty and Keroppi and Friends. I think those were their titles, anyway. ^_^; They used to be on YTV a long time ago, and now they're on Treehouse. =o I didn't watch them regularly, but I did enjoy them once in a while. ^_^; I think I also remember another show of the same general type, but I can't recall the name. o_O
There was also Dragonball. I remember watching it one night after Reboot. =o I don't remember liking it, though... lol. I think I was too young. ^_^;
Then there was this movie that I used to rent all the time. I LOVED it, and I found out either last year or the year before that it was an anime. It was called "The Last Unicorn" and I cannot seem to find it ANYWHERE now. ;_; I want to watch it so badly now... especially since it brings back such nostalgia of my early childhood and the fact that it likely was my very first anime... whether I knew that or not. XD
Then of course there was Sailor Moon. I think I knew it came from Japan, but I was too naive to think any further than that. It was just another cartoon to me... although it was basically my first "obsession". o.o; I absolutely adored that show. I taped almost all the episodes, I had the Sailor Moon bedding, the curtains, all the toys and puzzles... XD; I don't know where that stuff is now.
The first anime that I knew was an anime, though, was Pokemon... or Digimon. Probably both. o.o