Radiation is "in part responsible for the mutation that occurs in all organisms"*. In fact, I've heard little to suggest that there are any other significant [non-anthropogenic] causes of mutation (see previous post on mutation here).
Humans have happened upon this Earth about halfway through the planet's habitable lifespan. Putting aside terrestrial sources of radiation (both artificial and natural - they don't seem to figure significantly on the whole), it has been frequently noted that our atmosphere protects us from a large amount of cosmic radiation, solar and otherwise. The implication is that our atmospheric and solar characteristics dictate the "steady" rate of mutation experienced by life on this planet, which facilitates a stable - or life-fostering - evolutionary pace. It's interesting to speculate on the different radiation scenarios, and their possible outcomes. Too much cosmic radiation and mutation rates may go too high for good species cohesiveness; higher life forms may not develop. Too little radiation may mean insufficient adaptability to the planet's changing environment - Earth's environment for one has varied quite substantially in many directions over its history.
Given that we inhabit one of a very large number of solar systems in the outer reaches of our galaxy, it's plausible that other planetary systems may have developed along a similar path to ours. Speculation on how likely it is for there to be life anywhere near us would be a function of the density of our galactic neighbourhood, the likelihood of a similar solar system developing, and the range of tolerance of radiation for viable mutative life to evolve.
On an anecdotal basis (given the results of SETI to date), the suggestion is that there is nothing close by. But it would remain interesting to attempt the sums on the range of radiation that would foster an evolving biosystem.
*101 Key Ideas: Genetics, Jenkins, M (2000); Hodder & Stoughton, London.
This book has got some surprisingly sloppy writing and at least one incorrect diagram. But from time to time its descriptions give particularly useful insights.