Even if you don't smoke, you probably rely on your car's cigarette lighter to power at least one accessory. If this breaks or is acting up, you won't be able to charge your gadgets or use an external GPS system to find the best route to grandma's house.
Perhaps the socket provides power when you wiggle an adapter to get it to sit just right, but the slightest bump can break the delicate connection that you may have spent 20 minutes trying to establish. In this case, the problem may lay in the charger. Try another one if you've got it, or you can use a circuit tester to determine if the socket itself is the source of the problem. With the ignition switched to the "on" position, hold or clip the short end of the tester to the outside frame of the socket and carefully insert the longer end into the socket until it touches the back. Take care not to touch the sides, as this could blow the fuse. If the tester illuminates, then the issue probably lies within the external accessory.
If it does not, chances are that the fuse needs to be replaced. You can find a diagram of your vehicle's fuse box in the owner's manual to determine which of the many fuses is responsible for supplying power to the cigarette lighter. While the car is off, gently pull the fuse out of its position. You may need a pair of needlenose pliers to get a good grip on the fuse. Inspect it to see if the filament is damaged or broken. If so, you will likely only need to replace the fuse, but take care to purchase the right replacement, as a fuse with the wrong wattage could cause problems or blow as soon as you try to use the adapter.
If you replace the fuse and the adapter is still not working, there may be an issue with the wiring. Check to see if the interior dome light is working, as this is often controlled by the same fuse as the cigarette lighter. If it is, then the odds are that a wire may have come unplugged or even served as a snack for a tiny rodent.