My wife and I have become devoted Clone Wars fans; we watch it every week and really quite enjoy it. I'm the real Star Wars nerd in the equation, but the show has made her like Star Wars again (me too, come to think of it).
She has said on many occasions: "If only they skipped the prequels and went right to this show, Star Wars would be unequivocally awesome again." (She may or may not have used the word, "unequivocally.")
Like any show, not all the episodes are winners, but the writing is generally quite good, and surprisingly mature. I have come to love clone troopers, I like Anakin (finally), and despite a lot of fans' moaning, I really like Ahsoka.
I agree with others' comments that the stories add some much-needed depth and nuance to events that seem thin and hard to fathom in the prequels. By this point in season three, we have seen Anakin as more of a real person, and we can understand his plight much, much better than the seemingly awkward vignette presented within Revenge of the Sith.
Sadly, it's true that while GL had the best intentions with the prequels, the execution wasn't quite up to the task (I know, understatement of the year). And though this is not how I would have preferred things, I feel like the Clone Wars is patching a lot of those holes and smoothing out most of those rough edges, so that the grand story starts to flow again. It's not Shakespeare, but it's enjoyable.
Everyone's asking, of course, "What's going to happen to Ahsoka?" since we know she isn't in Episode III. I am more curious, besides, to know, "What's going to happen after Revenge of the Sith?" I would like a similar series to help that transition between Episodes III and IV be a little smoother than it seems right now.
I think Clone Wars proves that Star Wars really does work best when it's episodic and serialized—maybe if GL had gone this route after the OT, the story we wanted to see would have been much better represented.