Carburetors had long been a part of vehicle engines, but the last carburetors were used in United States engines around the early 1990s. With the death of the carburetor came the reality that idling a vehicle engine for more than 10 seconds is not worth the cost, environmentally or financially.
When engines idle
Engine idling happens in a variety of situations. While stopped in traffic, going through a drive-through or right after starting up an engine, most vehicles end up idling at some point. In many cold climates, people idle vehicles in the morning to warm up the vehicle and defrost the windshield. Before carburetors were phased out of most engines, this time to idle was necessary in order to help get the fuel mixture in an engine right, but most vehicles are now fuel-injected, which does not require a warm engine.
With most engines built after 1991, and all engines built in the United States after 1995, there is no reason to let an engine run for more than 10 seconds without turning it off.
Engines idling for more than 10 seconds are burning fuel, and re-starting the car does not take more fuel than idling would. However, keep in mind that in many municipalities, it is illegal to turn your car off if you are sitting in traffic, because it could be unsafe for other vehicles. If you are on private property, in a drive-through or otherwise able to safely shut off your vehicle when you are idling for more than 10 seconds, then you should do so.
How to de-ice without idling
The most often cited reason for idling a vehicle is to warm up the heater and defrost the windshield. Driving a vehicle normally for just 12 seconds can warm it up to the same level as idling for 30 minutes. Block heaters, which plug into a standard home outlet, can warm the engine to the point that a heater will be much more effective once you start the vehicle. There are specialty windshield wiper liquids that will melt ice and not re-freeze immediately.