Spiegel Online published a series of pictures titled "Desertec: Strom aus der Wüste" (translation: Desertech: Electricity from the desert). It includes this image of how much land would be needed to power the world, Europe or Germany with solar-thermal power.
The red square on the left is for the whole world, in the middle for Europe-25, and on the right for Germany. Below you can see pictures of the kind of technology they're talking about. It's a bit similar to Ausra's solar-thermal power system, but with curved mirrors. We're mentioning Ausra here, because they claim they're able to produce electricity from solar even at night (by storing some of the heat).
Of course, the transport of all the electricity to where it would be used is a serious challenge. There are ways to minimize losses, but over such long distances, there will always be some.
Still, even with losses and the massive challenge of building the infrastructure, this shows the potential of solar power. And the red squares in the first picture are just to show the scale, the real thing could be much more decentralized and located closer to already existing infrastructure (and not all of it would be in North-Africa, of course. There are many sunny deserts in North-America, f.ex.).
Lets not kid ourselves and claim that the red squares are small, but with the price of solar power falling (both photovoltaics (PV) and solar-thermal), it is starting to look more realistic all the time. We have so much roof surface where PV could be used, and there are many deserts where using lots of land for solar-thermal isn't a problem.
Of course, we won't get there all at once. But looking at how prices are falling and production capacity is increasing, we definitely think that solar power has a bright future!