One of the major obstacles is that you don't just need power, you need power on demand. Using current technology it's impossible to store electricity so it needs to be used right away or it's lost. Wind, solar and many other forms of green energy aren't dependable enough that you can rely on them as your only power source. If the wind doesn't blow on a winter night you're going to have a cold apartment if you're dependent on wind and solar.
There are experiments being done with transferring large amounts of electricity across countries in Europe based on the assumption that it will always be windy or sunny somewhere and that if power can be transferred long enough the uncertainty of supply will be cut drastically.
You can convert the electrical energy to other forms of energy though and store it that way. In following the link that nkurz gave the Andasol solar power station was mentioned which apparently will store excess thermal energy in liquid salt allowing electricity generation into the night. Pumped storage hydroelectricity is another, more established, method of storage.
I don't envisage huge vats of molten salt meeting our energy needs throughout the night but I suspect that energy storage will continue to have a part to play in meeting our energy needs in the future. It seems to be relatively expensive but then so is long distance transfer.
There are experiments being done with transferring large amounts of electricity across countries in Europe based on the assumption that it will always be windy or sunny somewhere and that if power can be transferred long enough the uncertainty of supply will be cut drastically.