In the movie Zombieland it is stated that it is at least two months since the outbreak and collapse of society, and yet every building, whether it be a country store or an amusement park, has electricity.
Most power in the U.S. comes from coal and gas power plants. Without people supplying more fuel, the plants would stop producing electricity pretty quickly.
Nuclear plants, dams generating electricity through water falling and windmills could endure several years without human supervision, as Randall Munroe, creator of XKCD states on it's funny book "What-if".
Also, many other energy plants could have fuel resources for more than just two months. Of course, this doesn't allow everything to be turned on but is enough to justify the presence of electricity on the story at the moment it's presented.
This has been addressed (or rather hand-waved) in the film's sequel. Apparently this is a world where self-managing hydro plants are the main source of electrical energy.
When Madison complains about it being a cold environment, Tallahassee suggests her turning it off, to which she replies that there is no switch, and that she’s just been waiting for the electricity to run out. It’s this comment that leads Columbus to chime in, “As long as it keeps raining, the dams keep giving us power.”
One assumes that this is in direct response to people constantly mentioning the presence of electricity as a plot-hole.
There is a national grid. Few people are using electricity. So perhaps if nuclear powers stations kept functioning there would be enough electricity to go around. Only one station would be needed.
