The likelihood of a causal link between the MMR vaccine and autism is insignificant. 10 of the 12 authors associated with Wakefields original paper have retracted their original conclusions, acknowledging that the data was fraudulent.
The reason that the MMR vaccine is associated with autism at all is principally because the age at which a diagnosis of autism can first be made correlates in time with when the MMR vaccine is given - around 12-15 months.
As an associated possible causative correlation, observers have noted a very large rise in the cases of autism that is now being diagnosed - up now to something like 70 per 10,000 individuals. This seeming rise though is largely explained by a broadening of the diagnostic criteria, to include conditions not otherwise described as autism in earlier times - So now we talk about Autism Spectrum Disorder.
In other words - the diagnostic criteria has widened, we are positively screening for it, and we are better at detecting it - all these are the primary factors contributing to what is seen as a dramatic rise. An environmental factor cannot yet be ruled out,but there are many possible candidates that are far more likely to be the culprit than the MMR vaccination.
Other indirect evidence to support the claim that the MMR vaccine is not the causal agent of autism; The proponents of such a link claimed that the actual agent was Thimerosal, a mercury salt used as a preservative. It was claimed that this minute amount of non-elemental mercury was causing neurological damage that lead to autism. As a precautionary measure, vaccine manufacturers removed thimerosal. So if this was the agent, we should have seen a reduction, or at the very least a levelling off in the instances of ASD - we have not.
Numerous case studies have been carried out that demonstrate no causal link between the MMR vaccine and autism. The most authoratitive organisation on trial data, the Cochrane Collaboration, recently performed a meta-analysis of all the studies and trials of the MMR vaccine -Studies which in total involved nearly 15 million children, to arrive at a series of conclusions about the safety and efficacy of MMR. Their conclusion with respect to a link between autism and MMR is that there isn't one.
Given this weight of evidence, given the lack of any plausible causal agent, given the broadening of the diagnostic criteria, the only reasonable conclusion one can draw is that there is no link. To conclude anything else absent decent evidence or a plausible mechanism would be speculation - which science allows for, certainly, but we do not attach much weight to it.
http://leftbrainrightbrain.co.uk/2012/02/22/cochrane-reports-vaccines-for-measles-mumps-and-rubella-in-children-review/