Wakefield's study from 1998 is now refuted as fraudulent, however there must have been subsequent research by others looking for a link between vaccines and autism. Did any of this research find a positive correlation?
The reason that Wakefield's study was found to be fraudulent is a result of the plethora of studies that were done after his. Not only could they not replicate the results of his study, but larger, better designed studies refuted the conclusion in his paper. Very large studies such as this Danish study found no correlation between the MMR vaccine and autism.
For more information, see the CDC's web site:
Some people believe increased exposure to thimerosal (from the addition of important new vaccines recommended for children) explains the higher prevalence in recent years. However, evidence from several studies examining trends in vaccine use and changes in autism frequency does not support such an association. Furthermore, a scientific review by the Institute of Medicine (IOM) concluded that "the evidence favors rejection of a causal relationship between thimerosal-containing vaccines an autism." CDC supports the IOM conclusion.
In a single word: No.
If anything, there is a greater correlation between autism and linoleum floors than there is to vaccines. Or even vitamin D deficiencies: What If Vitamin D Deficiency Is a Cause of Autism? (Scientific American, 24 Apr 2009).
If you wish, visit The Truth About The "Evils" Of Vaccination at factsnotfantasy.com for a point by point debunking of Wakefield and the errors anti-vax proponents like to repeat.
In my work on Rett syndrome (a neurodevelopmental disorder), I once came across a paper claiming that vaccination could be to blame for Rett syndrome. I'm rather ... skeptical about the paper.
On the other hand, scientists were able to put some parents' minds to rest about vaccination causing Rett syndrome. An Australian girl developed symptoms of Rett syndrome, and died of pneumonia at the age of 7 in 1991. In 2004, scientists analyzed DNA from a tooth they had kept, and confirmed she had had a mutation that causes Rett syndrome.
This was a relief to the parents, as she had been vaccinated a month before symptoms of Rett syndrome started, and she had a fall when she was 17 months - they were worried whether one of those things had caused their daughter's disorder.
(Declaration - I used to work with some of the people who retrospectively diagnosed the girl)
This one from 2011 did. It's certainly low impact and I haven't gone through it to find the flaws. I'd be interested to look at the data and see if there is anything there. The study has garnered strong condemnation for a variety of reasons.
Not a scientific study, but DHHS conceded that vaccines contributed to the autism-like symptoms of this neurologist's daughter. There is some more study to do regarding mitochondrial disorders, vaccination and autism, imho.