I was born in 1990 and the first anime I noticed before I knew it was anime and before we got cable, because I went to a friend's place who had cable:

Pokémon (4th grade)
Sailor moon (understood it in 4th)
DBZ (4th grade to present)
Tenchi muyo (saw this in 5th grade)

When I got cable:

Outlaw star (5th and 6th grade)
Blue Sub 6 (6th grade)