I usually care more about the writing in a show than it's animation, though I love a good art style as well. Basically, as long as it's not so terrible that it hurts my eyes, I'll give the show a chance.
I care more about the storyline, but if the voices are too annoying to listen to or the color scheme is too jarring, then I won't bother. Decent character (and background) designs are also important for me.
That's not my sole criteria on judging cartoons though. Writing and voice acting are also a big part of what makes a great cartoons or a terrible one. But without animation they'd just be radio plays.
Writing and characters are more important for me enjoying cartoons; however animation is still a factor in it.
It's better if the animation is better, nicer to look at,
but as long as I can at least see what's going on,
I'll watch to see if I like it in general.
You could'nt care less???? what if it was drawn by a 1st grader?
Considering animation is basically what a Cartoon is I would say its fairly improtant. I think a toons should have Good animation as well as good story & characters.