If i'm not mistaken my first anime was Arale and Dr. Slump, as well as Dragon Ball.
But the first anime that I saw knowing that it was anime was KALEIDO STAR
My Anime watching experience goes earlier than I would've thought. I was a kid living in Berlin Germany, and there were many Anime show shown on programs like Bim Bam Bino, and at the time I never really knew they were Japanese Anime.
I think the first Anime I actually watched and enjoyed was "Alfred J Kwak", because I learned just now that it was a Japanese Anime series based on a Dutch cartoon character.
Before I went to Germany I did see Samurai Pizza Cats on a Saturday Morning program but I never really watched it much because I never really gave it a chance.