The first reaction people have to the idea of an electric car (setting aside questions of cost, technology, etc., and assuming a basic respect for and awareness of the environment and associated issues) is exultation: "Zero emissions? Not just low, but zero? Sign me up!"
However, this proves to be a superficial analysis. How can a car produce zero emissions? Simple: the energy conversion processes which produced the energy that drives the car, and consequent pollution, were done somewhere else. If you consider only the car, you have a 100% improvement in pollution rates, but if you consider the entire system, it's not so clear. Now a power plant somewhere is producing more electricity to make up for the gas you're not pumping into your car. How are they doing?
Most power plants will be able to convert energy far, far more efficiently than you can in a car, because they can build much more sophisticated devices, thanks to economies of scale, both to convert energy more efficiently, and to better filter and reprocess the pollutants that result. Furthermore, some of the energy is being produced using methods that generate little or no pollutants into the air, such as hydroelectric, solar, and nuclear (yes, nuclear). So it would seem like they are bound to win the comparison.
However, the transmission of energy from their plants to your car's movement involves quite a few conversion steps, and each one of these involves a loss of energy. There's a considerable loss moving the energy down high-tension lines to your house, then more as it's moved into batteries in your car, and still more as it's moved back out of those batteries. If you calculate how much energy has to be generated to move your car, and how much pollution is generated doing so, compared to how much your car would have if it was gas-powered, the result is so close that you will find an electric car is a breakeven proposition in some parts of the country, a gain in some, a loss in some.
However, even this comparison is entirely unfair. If you are going to treat the electric car as part of a system and consider the pollutant output of the whole system, you have to do the same for the gas car. That means you have to add into your comparison not just the pollution your car produces, but also all the pollution produced by the drilling process, the tankers that move the crude oil, the refineries, and the tanker trucks that move the gas to your local gas station, and so on. And that makes the calculation tip heavily in favor of the electric car.
So after a lot of flip-flopping, we end up finding out that the first assumption turns out to be right. But that's only by luck. We still have to consider the question systemically; considering only one part of the system in isolation can easily lead to incorrect answers.