Interesting comments, all!
@Pyro - Smog and such won't be a problem, this hypothetical energy source is pollution-free. Also, I'm not too interested in debating the nature of the source, let's say it comes in little AA batteries that can power a house forever. Sounds crazy, but the question is more "what will we get up to when we don't have to worry about resources" than "how will this power supply actually work?"
@INow - Bigger and better guns is surely a possibility, but most (if not all) wars fought in modern times have been resource wars. Once there's no shortage, will there be a reason for another war, except as purely religious wars? Then a very sound argument can be made that the two main problems in the world is scarcity and religion. Wars wlil be fought over both of them, and very little else. So, as the world campaigns for the alleviation of hunger and poverty as a means to political stability in the World, we should (technically) also campaign for the removal of religion

- with which I fully agree.
@Buffy - I'm inclined to agree with you; if we remove scarcity from the equation, what incentive will humans have for getting out of bed? With unlitmited energy, full factory automation across the board will eventually lead to a redundant human race which will live in some sort of a welfare state which will keep them in submission with an endless supply of freely-made goodies. If everything is automated, the only cost will be the initial cost of setting the factory up - from there, everything is free. And the initial factory can be built by robots, removing even that cost. It'll cost you a single robot to convert the world to a paradise of sloth and obesity.
If that were to happen in the face of endless resources (energy, etc.), will the mere "love" of knowledge be enough of an incentive to learn stuff? You won't be remunerated with fantastic wealth for studying rocket science, there will be no reward. A reward is only worth something because others don't have it. You'll simply study rocket science because of an innate love of learning. I know that's what we'll do (we spend time at a science site for no financial gain, after all), but I fear we are in such a minority that we'll have to wade through crowds of fat, overweight, lazy morons in a permanent search for instant gratification just to get to the computer. (oh my God - the world will turn into AMERICA!!!) (Just kidding - couldn't resist

)
No, what I'm asking is basically "what's the next horizon?" Our current horizon as a global species is determined by limited resources. We struggle to get a plate of food on everybody's table. We struggle to spread literacy to everybody. We struggle to give everybody a fair deal and a fair chance. The majority of humanity is still living in conditions that prevailed in Europe in Medieval times. Us resource-using plane-flying car-driving literate slightly obese home owners are in the minority, the rest of the world is NOT LIKE US. Humanity's current struggle is for those NOT like us trying to become like us, and us trying to protect our interests in the process.
But what would be the next horizon after that one has been crossed?
Or, what would happen when all the "have-nots" have become "haves", and there's no resource or energy issues?
What will humanity do to bide its time, then?