I remember seeing glimpses of DBZ/Pokemon and then it got me curious and watch Makunochi No Ippo, and a few studio ghibli Movies, Akira when I was a kid. Good old days, then watched Naruto and I started to branch out from there.
Dragon ball and Pokemon were mine as well but what really got me into anime was Hunter X Hunter (2011) i started to really branch out and appreciate anime after that.