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?

>>26 is kind of on the right track, metals are good at blocking electromagnetic radiation due to their high electron density.  If the dome contained super high density plasma, as is found in inertial confinement fusion reactors, you could achieve as good of radiation shielding as a lead dome 10000 times as thick.