There's now been a court decision rejecting this claim.
The court said the evidence was overwhelmingly contrary to the parents' claims — and backed years of science that found no risk."It was abundantly clear that petitioners' theories of causation were speculative and unpersuasive," the court concluded. (AP) (italics mine)Lots of articles
This all bears a strange resemblance to the way that debates about evolution have also landed in the courts (in Dover, Pennsylvania, for example).
In both cases, the scientific evidence is out in the open, and quite lopsided in its findings, and so it should, in theory (maybe with the help of the press and the academy), be possible to arrive at a general public consensus. But that system didn't work somehow: consensus fell apart.
So now it falls to a court to reaffirm that the studies are sound, and that they show what they say they show: evolution is a really good theory, and there's no causality between vaccines and autism.
(This article links to an intriguing study which suggests that there could be some link between autism and TV. But it's pretty speculative, and it's just one study.)