I use my Garmin GPS regularly on flights. It works fairly well. I usually don't get questioned about it.

I use it with Street Atlas USA on my laptop. This gives a moving map that can be used to identify things on the ground. Not terribly exciting... But, it can be entertaining when you travel near significant landmarks.

You might have problems with your GPS on the Concorde if it is flying near its maximum altitude! GPS units that work at altitudes > 60,000 feet or 1,000+ knots are considered "munitions" per 22 CFR 121 (more details). Thus, it should not work at high speeds/alititudes.

This site lists airlines that are believed to approve the use of GPS on flights. (Note: Even if the airline approves it, the captain is still in charge!).

Here is a congressional subcommittee report on the topic: The Subcommittee on Aviation Hearing on Portable Electronic Devices: Do they really pose a safey hazard on aircraft? It mentions GPS as permissable above 10,000 feet: "In the middle of these two extremes are portable electronic devices that can only be operated before departure, while the aircraft door is open, or after the aircraft has reached an altitude of 10,000 feet. When the aircraft is descending, all PEDs in this category must be turned off. These actions are usually controlled by flight attendant announcements throughout the flight. The PEDs subject to these restrictions include CD players, laptop computers, electronic video games, and GPS navigation sets."