Although there is no concrete, scientific evidence of a link between vaccines and autism, the subject is still controversial.

Some of the controversy stems from research conducted by Dr. Andrew Wakefield who's findings were published in The Lancet medical journal in 1998. Wakefield's findings suggested a link between autism and the MMR (measles, mumps, rubella) vaccine. Later in 2010, due in part to an investigation by journalist Brian Deer who discovered that Wakefield's research was intentionally manipulated and flawed, The Lancet retracted Wakefield's published article.

Source:

(January 5, 2011). "Retracted autism study an 'elaborate fraud,' British journal finds". CNN. Retrieved 2015-02-01.

Godlee, Fiona. (January 6, 2011). "Wakefield’s article linking MMR vaccine and autism was fraudulent". British Medical Journal. Retrieved 2015-02-01.

According to For Parents: Vaccines for Your Children on the CDC (Centers for Disease Control) website:

Some people have suggested that thimerosal (a compound that contains mercury) in vaccines given to infants and young children might be a cause of autism, and others have suggested that the MMR (measles- mumps-rubella) vaccine may be linked to autism. However, numerous scientists and researchers have studied and continue to study the MMR vaccine and thimerosal, and reach the same conclusion: that there is no link between them and autism.

According to Vaccines and Autism on the Autism Speaks website:

Many studies have examined possible links between vaccination and increased prevalence of autism. This research has paid particular attention to the measles-mumps-rubella (MMR) vaccine, vaccines containing thimerosal and the total number of vaccines administered during early childhood or any one doctor’s visit. These studies have not found a link between vaccines and autism.

It remains possible that, in rare cases, immunization may trigger the onset of autism symptoms in a child with an underlying medical or genetic condition.

More:

• A Discredited Vaccine Study’s Continuing Impact on Public Health | The New York Times
• Vaccine Critics Turn Defensive Over Measles | The New York Times
• Measles Vaccines Don't Cause Autism -- But Unvaccinated People Create Outbreaks | Forbes
• Journal Retracts 1998 Paper Linking Autism to Vaccines | The New York Times
• Vaccine Court Awards Millions to Two Children With Autism | The Huffington Post
• Court Rulings Don't Confirm Autism-Vaccine Link | Forbes
• Autism-Vaccine Link: Evidence Doesn't Dispel Doubts | WebMD
• MMR vaccine controversy | Wikipedia
• Vaccine settlement no landmark, officials say | NBC News
• How the case against the MMR vaccine was fixed | British Medical Journal
• Italian Court Reignites MMR Vaccine Debate After Award Over Child with Autism | mercola.com