I hate the nerdy stereotypes. For some reason, all brainy types in cartoons tend to have coke bottle glasses, pocket protectors, horrible faces/complexions, buck teeth or other major physical flaws, and Mandark-like voices. High intelligence is definitely a good thing to see in both reality in fiction, but it can be excuted without stooping to stereotypes. I think Sally Acorn from the Sonic the Hedgehog comic is a pretty good example of a smart character who doesn't act stereotypically.
Also, going to the other end of the spectrum, I really hate stupid characters. Most stupid characters in cartoons tend to be a.) clumsy and inept in everything they do, b.) so exaggeratedly stupid that it's ridiculous, c.) fat, or d.) all of the above. God forbid a cartoon should have a character that's just "stupid" in a Forrest Gump way.
Racial stereotypes get me as well. For some reason, almost every black cartoon character seems to like rap/hip-hop, talk in Ebonics, and oh yeah, have huge lips and cornrows or an Afro. The comic strip Curtis is at least tolerable in that the author is totally out of touch with urban lifestyle in a funny way, and he does these totally bizarre Kwanzaa story arcs. As for, say, Proud Family, dat be one maaaaaad case of stereotypin', I just ain't down wit dat 'toon, girlfrieeeeeen'.
One stereotype that's always rubbed me the wrong way is the "invulnerable, nice-guy superhero/superheroine". You know, the ones where someone in a cape inexplicably has the ability to see through walls, fly higher than any airplaine, bend steel with his bare hands, read his doctor's handwriting, bowl a 300 every game without even touching the ball, do a cryptic crossword in under a minute, walk on the surface of the Sun without getting burned to a crisp, and oh yeah, always get the bland love interest at the end of the day without so much as getting pit stains on their shirt. Actually, I hate bland love interests too, or any female that's just there for eye candy or for the cardboard cutout role of "damsel in distress #436,897,125". Heck with it, I just hate gender roles in general. Let's see an athletic female for a change, or heck, a smart, sarcastic female with a dry sense of humor.
Of course, stereotypes are almost always acceptable when they're spoofed by capable parodists. I still haven't seen all of it, but I liked what I saw of The Incredibles just because of how it skewered just about every aspect of superheroes.