I find it fascinating that there is a huge machine up there, orbiting the Earth, with people living inside it. It's a tiny artificial world where living things survive through their own intellect and hard work in an environment where, from the point of view of nature, they are not meant to be at all and where they would otherwise be unable to survive.
I'm talking about the International Space Station (ISS). It is, in fact, surprisingly big. I would've thought it's at most the size of a bus, but it's bigger. Have a look at a size comparison to a Boeing 747 (from BBC). It may not look so huge, but don't forget that in a 747 one can't use the whole volume, as one is confined to two dimensions. But in orbit, one can utilize all three dimensions of the interiors (i.e. the whole volume), as it's a zero-gravity environment and there is no "floor" or "ceiling" as such.
Remember that ISS is not yet in its full size. ISS will grow even larger still, as new modules are launched to the orbit and attached to it. Overall, the volume will eventually be about the same volume as a 747, but will be better utilized.
Even though the ISS is a good start, it's not enough. Building an orbiting space station is the first baby step in ensuring the survival of the species. If mankind stays on this planet alone, it will be very vulnerable to major catastrophic events such as an asteroid hitting the Earth. This scenario is not so far-fetched as it sounds: to get an idea of the possible effects of an impact, one needs only to examine the K-T extinction event which happened around 65 million years ago. Although the impact might not have been the only reason for the events which spelled doom for the dominant species of the time (the dinosaurs), it surely contributed to their extinction.
The impact brought both death and life; it paved the way for small mammals, ultimately giving rise to new forms of life such as humans. Life itself as a whole is not under any kind of threat from asteroid impacts. However, a certain quite specialized form of life is. It is the humankind which has the most to lose.
A big enough rock would disturb the whole system of societies and the delicate planetary balance in a most profound way. One needs only to examine the descriptions attached to various levels of the Torino Scale, which is used to classify impact hazards. Depending on many things, such as the size of the rock, where such a rock would hit, etc., even a happy-day scenario might take humankind hundreds, if not thousands of years to recover, rebuild and adapt to the new situation. In the worst case scenarios there would not be a humankind after the impact.
However, an orbiting laboratory alone does not ensure that humankind would survive: the space stations we have (and have had) all rely on a steady service from the mother planet. The stations are not and have not been self-sufficient.
To be truly free of the "all eggs in one basket"-scenario, there must be self-sufficient, growing colonies outside Earth: Moon and Mars are very good candidates for such places. Growth is an essential element in this scheme. Even if an extraterrestrial colony would be self-sufficient in the meaning that it would not need support from external sources - it could create food, oxygen and water all by itself - without growth it could not accommodate for expansion and would at most stay as it is, or slowly athropy until it were small enough to die out completely. If the colony stayed as it is, there would be less redundancy among the population and the colony in general, and therefore an unfortunate accident might wipe out a big enough part of the colony to kill also the rest due to secondary effects.
For example, in a single colony, destruction of centralized food production (e.g. a fire breaks out in the greenhouses) would spell doom for the entire colony. In a suitably decentralized colony, e.g. with multiple self-sufficient colonies spread out, such an accident would only kill off one small part of the colony.
Even the creation of one colony requires substantial effort. As we currently have a hard time upkeeping even one manned space station in orbit it seems infeasible to send multiple colonies from the mother planet. It is therefore best that the colony will be able to grow by itself and reproduce all those parts which are needed to create a new colony. In other words, the colony must be autonomous. The only way to achieve the creation of autonomous colonies is through technological innovations and space research.
But what about the arguments like space research is too expensive and a waste of money, the money would be better off spent on Earth to do this and that, why go to space when there are hungry homeless people in my block, and so on? Many people say these things, but they do not analyse the situation any further.
Just to put things in perspective: for USA, the war in Iraq alone has cost many hundreds of billions of dollars, whereas the yearly budget for NASA lingers somewhere around 17 billion dollars. That's the whole NASA vs. just one theater of operations. The yearly budget spent for defense in USA for 2007 was 440 billion USD. The budget for NASA was about 3.6% of this. There is a nice site with a graphical breakdown of the US federal budget - see if you can find NASA there.
Of course, the problem exists outside the USA as well. Each year, trillions of euros are spent on war, crime, helping profit-making corporations with tax money, and so on. If one is intent on cleaning up the waste of money around the planet, there are surely a lot better places to start with than funding of space research and exploration.