If I remember correctly, the first non-kid friendly anime (like Pokemon or Dragon Ball) I watched was Blue Gender. Probably not the best way to start your otaku career as a 12 year old kid, but it's among the best anime related memories I have.
Back then, Sci-Fi channel still aired in my country and I'd stay up late on Friday nights to watch. I also remember Neon Genesis Evangelion and Martian Successor Nadesico being mixed in with that and the Giant Robo OVA somewhere in between, but I think Blue Gender was first.