GPS manufacturer Navteq says it does. They recently released the results of a study that they had commissioned that show that drivers that have a navigation system used less fuel on an annual basis then drivers that don’t.
The problem is, because the Navteq paid for the study, you have to be a little cautious about their objectivity. Personally, I believe it. Having used a GPS satnav to travel long distances, I find that I can get from point A to point B much more efficiently than with a printed map or directions. Of course, on a daily basis the only real benefit would be if your GPS had traffic avoidance. But If you can avoid sitting and idling for long periods of time, you could save some fuel there as well.