For the sake of clarity, even though most of us know this, in the US vaccine reactions are monitored in severalways. Two are the vaccine adverse event reporting system (VAERS) and vaccine safety datalink (VSD). VAERS is a passive monitoring system, any member of the public Congo to the website and report an adverse event. There are problems with it because things get reported that aren't actually related to vaccines and things that are related to vaccines never get reported. VSD is an active monitoring system.several (around a dozen) HMOS participate and medical records of patients in those HMOS are intoned for certain things, like increased primary care or urgent care visits after a vaccine. This system has a lot less "noise," but is still imperfect, of course. There are a few other monitoring systems, and other countries have similar systems.
You can read more about monitoring here: http://www.cdc.gov/vaccinesafety/Vaccine_Monitoring/Index.html
Several studies have attempted to use VAERS data to determine how common serious diverse events are. One can be found here: http://www.cdc.gov/mmwr/preview/mmwrhtml/ss5201a1.htm
This study found an adverse event was reported for 11.4 out of every 100,000 vaccines administered. Most of those were minor (fever, rash, etc). 14.2% of reports were serious, where serious meant death, hospitalization, lifelong disability, etc (see the link for more details).
Does this mean 14.2% of vaccines resulted in a serious adverse event? No!! 14% of 11.4 out of 100,000 did. 14% of 11.4 is 1.6. So 1.6 out of every 100,000 vaccines given resulted in a serious adverse event, or .0016%. That means for an individual child who receives around 25 vaccines (counting all the doses and calling each shot one vaccine for the sake of consistency) they have around a .04% chance of a serious reaction.
Hard to say how good that data really is, but there's one whack at it, at least.
I found some other info, one PDF from that same expert and independent panel in Australia that has been getting so much love around here lately: http://www.public.health.wa.gov.au/cproot/432/2/FS%20Vaccine%20Side%20Effects.pdf it breaks down the risks by reaction and vaccine.
I have some other stuff I want to post later, but I have to go get some work done for now!