I was going to write something else, but I couldn't pass this up...
I believe space exploration is very important. We have achieved great technological progress by exploring space; think about the Internet, teflon, etc. (Actually, not too sure how close the Internet was intertwined with the space program.) Space exploration irrevocably changed our entire history, everywhere; I can't think how it wouldn't be important.
There's also the part regarding resources. Earth does not have infinite of them. We're already running low on oil, where we may use it all up by 2050 (if not sooner.) But we also can't use internal combustion engines in space, so we have to develop new forms of power generation for up there. And have we! Solar power and nuclear power (even if the latter isn't truly in use yet). We need to go elsewhere, to find new sources of materials. The moon, for example. Mars. The asteroid belt. Mercury (at least for solar energy.) Earth will not sustain us forever.
Also, we're running out of space for people. Now I realize with arcologies and such, Earth could support a lot more people. Our problem now is that we're not managing our space very effectively, a problem we've only really had to face since the end of WWII. But, we're not going to manage it effectively. We want big, open yards. We don't want to feel closed in, we don't want to live in arcologies. Which means that eventually, we will use up all the space on Earth. My solution, of course, is to live in orbital habitats, which probably sounds paradoxical at this point since I just mentioned we don't want to be cooped up. But its a reason why I feel space exploration is vital, so that we can establish habitats off-Earth, so the human race can expand.
Oh, and there's the whole "backup" concept, in case some tinpot politicians nukes the planet or we get hit with a giant asteroid or 4chan happens to escape its confines, then we're going to need settlements elsewhere if the human race is to survive. (Yes, I just labeled 4chan an existential threat to humanity. Deal with it.)
But I doubt that government is the right way to do it. What happened after we landed on the Moon? We kept going for a few years, then stopped. Since the early 80's, space travel has stagnated. Part of this, I feel, is due to politics. Politics must incorporate the entire opinion of the public, and quite frankly, the public lost interest in serious space travel (it needed sharks with laser beams in order to grab their attention.) Since then, space projects have been generally failures, or at least unambitious. They've also been quite inefficient.
I think that private space projects are just the way to go. You see the innovation every day in the world of technology from private groups, from guys who just have kooky ideas in their heads, not from giant government agencies. It would also allow those who don't believe in space flight to hold onto their own resources and spend it on what they deem valuable, while allowing those who want spaceflight to continue to invest their own resources and push forward without politics getting in the way. A win-win situation for everyone, no?