I believe that MMR (triple dose) immunisation has a reasonable safety profile from the available evidence at the moment. Two of my three children have been given the MMR immunisation. The Department of Health recommends MMR immunisation. Information can be obtained on their website at http://www.doh.gov.uk/cmo/cmoh.htm
Some concerns about MMR immunisation stem from the research of a group at the Royal Free Hospital led by Dr Andrew Wakefield, who have suggested that both the measels infection and measels vaccination can be associated with an increased risk of Crohn's disease (an inflammatory disease of the bowel), and that the MMR vaccine may be associated with the development of Autism (a disorder frequently diagnosed in the second year of life) ...