I agree with the "more than four limbs" idea, not so much with them being the typical, fat little fuzzballs with oversized eyes... That kinda got old a long time ago, about the same time as furbies went out of fashion.

I think they should be more like ferrets, with snake-like bodies, dozens of paws and puppy-dog faces. And they should be all stretchy and tie themselves in knots chasing their tails! And purr like cats when you pet them!