For some reason, I have not found any information on using a GPS to help avoid runway incursions other than mentioning it myself in my book, Cockpit GPS, which is available from the home page of this site, www.cockpitgps.com. Sure there is discussion of new technologies based on GPS, but not simply using the map display to help you from getting lost on the runway.
What kind of GPS do you need? Any aviation model that shows a runway diagram will do. I will provide some screen shots from a Garmin GPS III Pilot, because it is among the more humble, yet viable receivers.
The technique is simple. Zoom in on the mapping GPS so that you see the runway diagram. All that you will see is a simple depiction of runways, not a whole airport diagram. However, this is very helpful to orient yourself and double check your location on the airport. Turning on the wrong taxiway is embarrassing. Turning onto an active runway can be catastrophic! In no way am I selling this as a substitute for using the airport diagram, but as a tool to help keep you oriented on the diagram. This is also not a simple cure for all runway incursions. It is just one more tool that is available to right now that can help with the problem.
I should also add that common sense and conservatism should always prevail. The runway diagram in the GPS could have inaccuracies and the GPS position could be in error, but generally I have been impressed. If the GPS shows that you are coming up on a crossing runway, you probably are. If the next piece of crossing pavement looks like a runway, but the GPS runway diagram does not show it as such, go with the conservative assumption.
I also fully realize that many runway incursions do not occur from being lost. However, being lost is a factor in many incursions. Also, the more concentration you can free from trying to orient yourself, the more of it you can spend on listening to the controller to make sure that you hear and comply with hold short instructions.
It is possible to set up a Tablet PC or a PDA along with a GPS and the right software and get a full airport diagram -- I think some of the Jeppesen software will do this. Honeywell has an upgrade to their EGPWS system that provides voice warnings such as "approaching runway 26." Airports are installing various ground systems also. These new technologies have much potential. My point is that the GPS that many people are already using can provide quite a bit of situational awareness on the ground as well as in the air.
To illustrate my point, let me give you an example that was almost a terrible accident where I disorientation was obviously a factor.

Here is the synopsis from www.ntsb.gov/Recs/letters/2000/A00_66_71.pdf:
After UAL1448 landed on runway 5R, the PVD local controller instructed the flight crew to exit the runway to the left, proceed to the ramp via taxiways N and T, and report when the airplane crossed runway 16. The UAL1448 flight crew became disoriented and turned back toward runway 5R. The flight crew then stopped the airplane, advised the PVD local controller of its position, and stated that it believed that the airplane was on an active runway. While UAL1448 was deviating from its assigned taxi route, FDX1662 departed from runway 5R, passing near UAL1448. (The sound of FDX1662’s takeoff can be clearly heard in the background of the ATC recording of UAL1448’s transmission of a position report.) Although the flight crew of UAL1448 reported its belief that the airplane was on an active runway, the PVD local controller cleared US Airways flight 2998, a Boeing 737 (737), for takeoff from runway 5R. The 737 flight crew declined the clearance because of its concern about UAL1448’s position. The incident occurred in IMC at night. No injuries were reported, and neither airplane was damaged.
If you would like a better airport diagram, click here. On this diagram the taxiways have been re-designated, but you can still get an idea of the intended route to the terminal.
The windshield heat on the 757 will block the GPS signal rendering it almost useless. It might surprise, you that the 757 does not depict an airport diagram -- for that matter, neither does the 777. I believe that there should still be an amber line depicting the approach, but I am not sure. My point is not how this exact case could have been prevented, but how you can use a mapping GPS to help prevent you from a similar situation.
Here is the display from a Garmin GPS III Pilot turning off the runway:

Here is the display that the UAL pilots would have seen when they were approaching the incorrect runway after making the wrong turn:

This is what the GPS would show if they had made the correct turn and were crossing the correct runway 16/34 which was closed:

What I have not shown is that most handheld GPS receivers show a "bread crumb" trail which makes orientation even easier. Most IFR mapping GPS receivers do not have the trail, but they do have the approach to the runway depicted which aids in orientation.
The NTSB has tower tape with some animation in Real Player format at: http://www.ntsb.gov/events/2000/incursion/pvd_incursion.rm.
However, I much prefer the AOPA Air Safety Foundation's Flash presentation of this scenario. The animation is complete with an airport diagram showing positions of the various aircraft involved along with the tower tapes.
I quickly stepped through the program. I thought there were some excellent points. On the issue of GPS usage, it advises you not avoid the distraction of GPS operation while taxiing. Basically, the point is that you should not distract yourself from by such tasks as programming flight plans into the GPS -- I wholeheartedly agree. However, I feel that using the map display zoomed in to show the runway diagram is a great help to situational awareness and is a simple enough operation not to be distracting.
Although I told you how to get to the portion of the program that illustrates my point, I would recommend taking the time to go through the whole program. It appears to be a good program, just consider also zooming in the GPS to help build your mental model and maintain situational awareness.