I know a lot of people keep mentioning Tom & Jerry, but keep in mind it's not a true 80s cartoon. It had been around for decades before any of us were even born, just like all the Merry Melodies.
For me, when I was growing up I would watch:
Eek! the Cat (I still try to find episodes of this show, it was ungodly funny)
Animaniacs (Reader's Digest voted it "Coolest Cartoon on TV" 2 or 3 times, it was one of the first cartoons that bridged the generation gap and made adults laugh just as much as kids)
X-Men (oh fuck I can hear that theme music in my head right now GOD that was a good cartoon)
Ghostbusters
Duck Tales
Chip & Dale Rescue Rangers
I didn't have cable, but whenever I could catch Ren & Stimpy I did. At one point, I downloaded every single episode in the series along with some never aired ones, about 10gigs in all. Fucking awesome.
And, finally, the mother of all 90s cartoons... the Tick. I dare anyone to watch an episode of that and not laugh, it was pure genius. (Well, the first season was... then Arthur's voice actor changed and it started to kinda suck.)