That Wikipedia link is a good starting point. However, the whole issue of the effects (if any) of free radicals upon health is controversial.
Some researchers have suggested that free radicals, produced when the body fights infection, are a possible cause of cancer and/or the body's ageing process. It's known that antioxidants, such as Vitamin E, can 'mop up' free radicals, so it's been suggested that increasing the consumption of Vitamin E can provide a certain level of protection against cancer and/or ageing.
However, most people already have sufficient Vitamin E in their diet to mop up the free radicals in their system. Increasing Vitamin E intake is (for most people) at best pointless or, at worst, positively harmful:
http://www.bioedonline.org/news/news.cfm?art=1 374
Even the whole theory of free radicals being harmful is now seriously questioned by many researchers:
http://news.bbc.co.uk/1/hi/health/3485508.stm
Chris