That's the problem Germany is trying to solve as part of its "Energiewende" policy. Phasing out nuclear energy switching to renewable energies.
Due to the power fluctuation inherent to wind power the maximum capacity of power production needs to be about double as high as it is today. That way you can store the excess energy produced during peak times.
How to store it?
Short-term: Batteries. Only good to counter-balance short power fluctuations. Also expensive.
Medium-term:
Pumped-storage hydroelectricity. These are in use already. You basically pump water to higher elevations during power production peak times of wind and solar power plants. When their electricity production decreases (less wind/less sun) you use that water to produce electricity.
Long-term: Power-to-gas technology. You use excess power to produce hydrogen by electrolyzing water. The hydrogen gas is then co-mingled with natural gas in the existing natural gas infrastructure, namely the gas pipeline network and its associated underground storage facilities. The German
Fraunhofer Society (a big group of research institutes) has been conducting research here for quite a while. The basic technology is ready for use but the power equivalent of a barrel of oil still costs about $150-200.
Fraunhofer info on power-to-gas. I suppose the costs will decrease once the technology gets more mature, while the oil price is probably going to keep rising.
Advantage: You can use the existing gas infrastructure and it only takes about 20 minutes to power up a gas turbine in a gas plant. Pretty flexible tech.
Sidenote:
RAMA's ramblings about nanotech are obviously science fiction but I figured I'd bring him up-to-date to actual technology and solutions we're currently working on.
Oh, and this isn't an easy transition process. It's going to be very expensive but if we're lucky the effects of peak oil will take a couple of decades to manifest completely.
But even then: I suppose a country like Germany can make the switch and they're the first to actually work on this. The transition costs will decrease once these first steps are done so it'll be even cheaper for other countries (while Germany could make a profit from selling technology and expertise).
But I'm also sure that some countries will fail at implementing the changes fast enough. These things are long-term but even then there's the possibility of a major crash in economy either in unlucky countries or (more unlikely) world-wide. The technology is there (at least in part) but you need the political will and society needs to be willing to take on the costs. Good luck with that, America.