Hard to say which anime I have seen as first one. I remember three of them from my childhood: Sailor Moon, DragonBall [no surprise I think] and my fav one: Saint Seya <3.
However, the anime I started seriously watching as a teen, was Shaman King on Polish channel for kids Jetix
. I must admit I always loved anime, but sometimes had to watch it hidden with my lappy somewhere, 'cause my dad used to call anime 'these stupid Chinese [yes, Chinese~! o.O] cartoons' xD.