Colonizing the Moons

Logistics aside, would it really be possible to colonize the moons of the gas giants?

It's my understanding that planets tend to have radiation belts around them.  Would the massive radiation from a planet like Jupiter make it impossible to live on its moons or are some of them outside this belt?  Or could people just live in protected domes of some sort?

>>8
There had better be a good reason, such as mining uranium.
Are you kidding? That's not a good reason at all. There's already shitloads of uranium on Earth. It's abundant here. Why go all the way to some moon to get it?