Its true, the energy has to come from somewhere. However, large scale power plants are typically much more effiecient then car engines. Also, depending on your local, power sources can be solar, wind, Nuke, etc....its not all coming from smokey brown stuff.
Additionally, pollution from centralized power plants can be more easily controlled, and at the very least localized.
And even if your power bill does rise, it will still be cheaper to power your car...and in the end, save you money. That is, assuming you own an electric car.
BTW, my local power grid punishes me if I use more power, not my neighbors. My rates rise based on my power usage, and my purchase of an electric car would not impact the bills of others. Also, its extremely unlikely that the power grid would suffer from electric vehicles, as the adoption rate of such cars would be rather slow...providing plenty of time for the power grid to expand to meet such demands.
All that said, I live in an apartment...so I can't own an electric car.