As gcatalfamo and yareally pointed out, Disney had Duck Tales, Darkwing Duck, Chip n Dale and so on.
Meanwhile at Warner Brothers they had Tiny Toons, Animaniacs and of course the excellent Batman: The Animated Series. I rewatched it recently and, unlike a lot of my nostalgic favourites, it has held up beautifully.
MTV backed Beavis and Butthead and Aeon Flux. Fox backed King of the Hill and was riding the wave of some of the best of the Simpsons.
And let's not forget Klasky Csupo -- most famous for Rugrats and Aaahh!!! Real Monsters, they were also responsible for my favourite "cartoon for grownups", Duckman. I love that show -- if it'd been around for the DVD era we'd probably still be watching it.
Edit: and Nickolodeon (forehead smack) with The Ren & Stimpy Show and Rocko's Modern Life.