There have been many studies regarding the increase in number of vaccines. Most importantly, although more vaccines are given there is LESS exposure to the immune system. In other words, the number of Proteins and Polysaccharides in vaccines have decreased as seen below:

• 1900 - 200 Proteins (from Smallpox Vaccine)
• 1960 - 3,217 Proteins (Mostly from Whole cell Pertussis Vaccine)
• 2000 - 126 Proteins (decrease due to Acellular Pertussis Vaccine)

In 1960, there were vaccines for 5 diseases commonly given. Since 2000, we vaccinate against 11 diseases. As can be seen above, there is less than 4% of the number of proteins now given as there were given from 1960 to 1980. Other studies done also show no support to the idea that multiple vaccines overwhelm, weaken, or “use up” the immune system. On the contrary, young infants have an enormous capacity to respond to vaccines and everything else in their environment. By providing protection against these diseases, the vaccines prevent against the serious complications and death due to the natural infection.

Reputable CDC link to research about vaccines and autism
http://www.cdc.gov/od/science/iso/mmr_autism.htm