You know, i have often been thinking about how hard "90's cartoons" are to define compared to all other decades (when talking about American cartoons, anyway). It's like, the majority of what was made in, say, the 40's looked and felt quite similar, and it's the same deal with the 60's, the 80's ect. And it's also true to a very big extent today; even though there is still more variation in genres and styles when it comes to cartoons today compared the pre-90's era, there is still a certain genre/style (at least when it comes to television cartoons) that i feel is present in a high enough percentage to be considered the defining style of the 00's and beyond. Namely, the (usually first and foremost comedic) cartoons drawn in a very flat, stylistic and usually edgy style.
As for 90's cartoons though, the variation in looks and content was extreme compared to all other eras in American animation. On a given week in say 1993, we could have shows as diverse as Batman TAS, Ren and Stimpy, Beavis and Butthead, Teenage Mutant Ninja Turtles, The Simpsons and Animaniacs.
However, if i would nevertheless have to choose one genre to represent the decade, i would probably go with what i call the neo-golden age comedies. That is, the very "cartoony" comedies that to varying degrees attempted to emulate the "squash and stretch" animation and "anything goes" approach of the golden age (and often made just as heavy use of "Mickey Mousing" as the golden age shorts), but nevertheless also updated their style of comedy with more verbal humor, pop-culture references and gross-out humor. Some of the most triumphant examples of this are of course Ren and Stimpy, Tiny Toons and Animaniacs, with further examples being Adventures of Sonic the Hedgehog, Taz-Mania and Timon and Pumba. If a kid today asked "what was cartoons like back in the 90's?", showing an episode of any one these cartoons would probably be a valid reply.