(I hope someone reads this. It took a while to put this together.)
IMHO, cartoons are great when they make the best possible use of the fact that given how
everything about it is fictional (i.e. it's not the real world or anything close to it no matter the similarities), it can go as crazy or over the top as it wants, especially if it's for comedy's sake. Of course, you still need the obvious elements such as likeable characters, room to grow, interesting story, etc. Sure there are things like story, where quality depends on the intention (comedy = not so much heavy stuff.)
So to me, any cartoon that doesn't embrace that, or if it does without care or quality, sucks.
Another thing that sucks: when the characters, mainly the protagonists, are complete morons for the sake of being complete morons and staying that way. And when they emote, it's dumb and obnoxious and has no impact whatsoever. It's the worst kind of one dimensional character one could create. I understand that there are characters like say, Homer Simpson, who IS a moron, but NOT one-dimensonal. He's the way he is mostly because of sitcom standards, but at least he's funny for the most part (that's where good writing and comedic timing comes in, I know). Plus, there are enough moments in The Simpsons 20+ year history that have shown Homer to have a wide range as a character, moments where he's genuienly concerned about being a good husband, father, son, helping someone out, etc. even if it's for something he provoked, which is more than I can say about that bastard Spongebob.
Through my little brother, I discovered a show on Disney Channel called Phineas and Ferb. I can understand why some don´t like it, mostly probably because of the rigid structure set for almost every episode and it's reliance on repetition. But for whatever reason, I have been enjoying it. A lot. It's just fun and it works FOR ME. The comedy is well timed, the dialogue is funny, it's silly without being stupid (mostly), the characters are likeable (the best part of it), and it's eponymous characters ARE NOT IDIOTS. Basically, I kinda feel about this show the same way Moviebob feels about the G.I. Joe movie.
http://www.escapistmagazine.com/videos/view/escape-to-the-movies/866-G-I-Joe-The-Rise-of-Cobra
The creators have done work for shows like The Simpsons, Rocko's Modern Life, and Family Guy. I just wanted to bring this up since it's been on my mind for a while.
Aaaaaaaaanyway..... if I had to pick the worst animated series, it would probably be Spaceballs: The Series. It was supposed to be an animated spinoff of the Mel Brooks movie, characters and all, on G4. But it was SO BAD, that it only aired a single episode. All you need to know is that the episode's title was "Lord of the Onion Rings".
Before anyone brings it up, I know I focused on comedy rather than cartoons with a more dramatic edge (Anime mostly), but it's only because the fun factor is my main draw when it comes to cartoons.