Humans are explorers by nature (literally). For a very long time, the Earth was filled with new places and undiscovered wonders. But we're at the point now where we can literally "see" a birds-eye view of almost any spot on Earth - without even getting up from our seat. The month-long journeys across the oceans are now a few hour airplane flight away. We're quickly outgrowing our container, and to remain here indefinitely will cause stagnation of our species.

That was the romantic angle - there are many others, such as the practical angle (we're using up natural resources with a minimum effort of conservation). Plus, as Sample stated in Comment #1, the Earth will die one day (or at least the parts of it that we rely on).

Now I don’t know about you, but were I born on Alpha Moon Base I’d want to get the hell out as soon as I was old enough to realise that a place existed with blue skies, oceans, sunsets, girls in grass skirts on tropical islands, rain, wind, snow, mountains, deserts, and a respectable quota of gravity. Yes that’s right, the place everyone was so eager to get away from. That discarded blue orb in the sky.

Perhaps this is true of a moon base, but just think of the wonders that await us if we somehow discovered a method of interstellar travel. We can try to imagine it - but we can't, because our only frame of reference is what we know from this planet (and the tiny bits our scientists can discern from looking outwards). There might be wonders out there that blow grass skirts and small mountains away completely.

Of course, the chances of such a future are slim (in my pessimistic opinion). The bulk of humanity would have to wake up from it's primitive, superstitious, ignorant mindset. We'd have to avoid/survive pandemics, natural catastrophes, and resource depletions. We might never get there, but at least the passion and desire for this goal will drive us forward (your typical "more about the journey than the destination" scenario).