In response to Rays comment about the power grid not being able to handle the exta demand if every one were to plug their electric cars in to recharge at the same time, a lot of work is being done in the field of "smart charging". This is where the plugged vehicles will not draw their maximum current when there is high demand on the grid. This will even out the demand. In addition there are concepts where the vehicles that are plugged in and are close to or fully charged may deliver some power back to the grid at times of peak demand, to ease the load on the generators.
Most ordinary domestic supplies are rated by the incoming supply fuse to 100A. In practice the peak load will be around breakfast and early evening when cookers kettles and electric showered are used. That may be a peak power of about or 60A, and the grid power lines don't melt, so whilst the generators may struggle to match the demand, the actual wires can handle it. The biggest domestic car chargers are unlikely to be need more than 32A and often will only be 13A, so it's not going to test the Wireing in most houses and localities
There is also the Tesla power wall concept, where properties will have a battery pack, which can be charged from solar or off peak power, and that then provides the power to charge the car, or as above help relieve the generators peak demand.
In many ways the generators will like the idea of smart charging, as it will even out the demand, (and of course they will make more money)
There are definitely challenges ahead; there may be infrastructure problems in some locations, but the biggest difficulty will be changing the publics mind set about how we use, make and store electricity.