It saves a lot of gas too. I've always tried to get through stop and go traffic smoothly without using the brake, but I always did it for my own gas consumption. I never had this macro look at it.
Especially if you drive a standard transmission. Staying off the brake makes a huge difference, and makes for less clutching as well. For bonus points, you can put the car in neutral while coasting, although some don't think that's safe.
On modern cars with manual transmission, the motor is powered with some gas when it is not engaged. However when you leave it engaged an just don't push the pedal, no gas is needed. (Although the motor brakes somewhat. I don't know which effect is stronger.)