It seems to be happening less frequently to me of late, but I've found that on a significant number of cars I rent (20%) that the fuse for the cigarette lighter is burned out. And so I've taken to traveling with a few spares, to keep my GPS and other devices powered up.
Most rental cars use what are called "minifuses". If the cigarette lighter isn't producing power, head to a local Target or the like and buy their variety pack, about $4. The one you need will be in there.