Oh gosh. I saw a couple episodes of Fushigi Yuugi at a friend's house when I was younger and I was both super weirded out and kind of intrigued.
First anime series I actually sat down and watched was Trigun, I think. To this day I've still never watched Sailor Moon, Pokemon, DBZ, Yugioh, and most of the TV ones you'd think people would watch. ^^;;