I never really watched DBZ when I was younger. The only anime show(s) I really got into were Inuyasha, and YuGiOh, and some others I forgot.
I was all over Inuyasha though, I miss the good ol' days. ;(
When I was younger it was pretty much the following :
DBZ,Yu-Gi-Oh,Digimon,Pokemon,Shaman King,Beyblade and yea some others I can't quite remember but were really popular as well.