During the late 80s/early 90s, I quite enjoyed the Disney cartoons that were popular at the time: Ducktales, Chip 'n' Dale Rescue Rangers, Tailspin, and Darkwing Duck. I'm sure I'd still reasonably enjoy them, but I haven't felt any particular urge to rewatch them as an adult.
I also liked the Teenage Mutant Ninja Turtles cartoon of the same period, although I stopped watching it before it ended. I think, as I grew up, I started to prefer the more serious takes on the Turtles mythology, such as were found in some of the comics and the first live-action movie (not that there still wasn't some humour, but it was definitely less goofy and cheesy than the animated series).
The mid-90s is when some of my favourite cartoons came out. Gargoyles is, bar none, my favourite. It was much darker than the average Disney toon, and it got me interested in a wide variety of subjects, including Shakespeare, ancient mythology, and medieval history. It was such a great show -- I'm so pissed that Disney never released the second half of Season 2 on DVD! Yeah, you can find the episodes on Youtube, but it's not quite the same.
If there's room for CG animation shows, I also love ReBoot, from the same era. It was so much fun, and there's a ton of references that I never caught as a kid. I especially liked it after ABC decided not to air any more episodes after Season 2, which turned out to be a blessing in disguise. The show continued here in Canada, where the producers were free of ABC's uptight censors and took the show in a darker, more adult direction. I'm still annoyed, however, that the fourth season was cut short for whatever reason, and the show ended on a major cliffhanger. I hear there might be some sort of revival in the form of a trilogy of movies, though, so I hope they can provide some closure (even though they will have to get a new voice for Megabyte, since the great Tony Jay has passed on since then). If anyone's curious, all of the episodes of this series are on Youtube as well.