If you are interested in my reasons and my opinions on much of the "research" people use to decide not to vaccinate, I have posted in many of the dozens of threads that ask the same question you ask.
There is very little factual scientific information out there that is not supportive of vaccination. Plenty of anecdotal stories and websites like Mercola and others that purport to provide scientific evidence. However, almost every article posted on these blog and non-science sites is distorted or doesn't even follow any sort of scientific process.
Look at the information out there. But, if you do not have a firm understanding of how to read statistics or scientific studies -- ask someone who does before believing whatever you read. I recommend bringing any questions to your doctor. And, if you cannot do that, then I would suggest that it's time to find a new doctor. But, don't be surprised when she shoots down most of the anti-vax arguments because most of them are spurious.