I estimated a car burns about 0.8L of gas to make one kW-hr of electricity. You could also use a storage battery, and charge it on the grid.
In Canada the cars have DRL's, which are lights up front running during the daytime. Instead of doing this by running the headlights at reduced voltage, making them incredibly inefficient at making light, you could use white LED's, which are about as efficient as fluorescent lights.
The DRL's use maybe 80 watts of power whenever the car is in gear. That requires about 100W of mechanical power going into the alternator. If a car uses 15 hp to move, on average, 100 watts is 0.8% of the average engine power. If you cut that to 0.19% by using white LED's, that would save more fuel than switching from 5w30 to the more expensive 5w20 motor oil does, but at a cost of only about $20 per car over it's lifetime. Some cars use special small light bulbs for the DRL, which is more energy efficient than the headlights, but it's still not the best choice, economically, since even 50 watts over the 4000 hour life of a car will cause about 160 L of extra gasoline to be burned.