Does it have to be cartoons? Or just any show?
I've avoided a lot of the cartoons from when I was a kid, mostly because I am guessing they will not hold up in any way. Some bits from GI Joe that I remember are things I'll quote to my friends to get a laugh, mostly Shipwreck's lines. For some reason, one of my friends finds it hysterical when I say, in the shaky voice, "It's me! Uncle Hector!"
All the cartoons I watched as a kid were basically 30 minute toy commercials though. All the 90s superhero stuff you guys are talking about was when I was in high school or after. I have actually never seen an episode of the Batman animated series.
The old Hulk and Spider-Man and his Amazing Friends cartoons were pretty awesome. Stan Lee addressing the true believers...kinda creepy, but yeah.
One show that doesn't hold up at all, at least as far as its current version, is Electric Company. Man that got really horrible.