Yes, for all the reasons above! Plus a few more:
1) Prevention of extinction through war. Even if we hold our population to it's current number (6-odd billion), the planet's resources will dwindle over time, and humans will fight over the scraps that remain. I doubt seriously too that nuclear weapons (or other WMD) will ever completely vanish, so that spectre hangs over us too. And as resources and prosperity dwindles, there will be more groups of desperate, fanatical, and apocalyptic-minded people that would have no qualms about using such weapons (to quote Dylan, "when you ain't got nothing, you got nothing to lose").
Whereas interstellar or even interplanetary war would be relatively difficult. Particularly interstellar, if relativity holds true at least for awhile--lots can change in the time it takes to traverse to other suns on a warship, at near-light-speed.
2) A chance to "start again". Imagine if earth were settled by us KNOWING WHAT WE KNOW NOW--i.e. about environment, social stability, etc. We wouldn't botch up other planets necessarily, because we'd know a few things NOT to do, or habits NOT to get into. It may already be too late to erase much of the damage we've done on earth--but if we can get a second chance, wouldn't you take it?
And knowledge of space is, I think, key to knowledge of environmental problems. At the very least, it helps us see "the big picture" better. Studying Mars may prove very useful here too--some believe that this planet was once earth-like and full of water, and probably bore life, billions of years ago. If so, what happened? Getting this story can surely give us insight into any climactic changes here on earth.
As a libertarian, I am generally loath to huge government spending--but I make an exception for space (unlike some other libertarians). I wouldn't mind more private participation in this though--and in the coming years we may see this too. But if we have ANY survival instinct at all as a species, we need to get out there, look around, and find some more lebensraum, so to speak.