Haven't read all the responses, but in case nobody's said it: the moon will never be easily terraformed into a stable environment, so the primary reason for moon habitation, aside from telescopes which require no fuel for orbital maintenance (and have no atmosphere with which to contend), is that the moon is a significantly easier place both to construct and launch rockets, so if we can get asteroid mining going, a moon base would allow significantly increased accessibility for rocketry for other missions.

For Mars, I figure it's twofold:

1. don't have all your eggs in one basket. If earth becomes uninhabitable for some reason, having a self-sustaining population on Mars could be the only hope for continuation of the human race.
2. direct study of Martian soils and other samples to determine if life has ever existed, or even currently exists, elsewhere in the solar system.

As someone pointed out, however, the current society is so focused on funneling wealth and power to only a few prime exemplars of the Dunning-Kruger effect, that to attempt actual colonisation when they are the ones who'd control the colonies would be violently, unbelievably stupid and be even more likely to lead to total extinction of life on Earth