The Global Positioning System, or GPS, is a very handy thing. One piece of modern technology that really is beneficial to everyone. "But if TSHTF, it won't be around anymore" you say. Or will it?
The Global Positioning System is comprised of a bunch of satellites that are in geosynchronous orbit, that is, they're revolving with the Earth, not around it. Meaning that they're always in the same general spot above the Earth, 24/7/365. These satellites are solar powered, and generally autonomous in their operation, meaning that they can hang up there and do what they do, with very little, or no input from the ground, for quite some time. I believe GPS will still be viable for years, maybe even decades after a TEOTWAWKI event. It depends on the lifespan of the satellites.
That being said, GPS ain't the be all end all, and should not be relied upon as your sole method of navigation! Good conventional navigation skills are still essential if you plan on doing any wandering about, by land or by sea.
For the unindoctrinated, GPS receivers (the thing you go buy) work by triangulating (at least) your position via the signals it receives from those satellites up there. Most times your receiver will get signals from more than 3 satellites, and this is good because accuracy is increased with more satellite "fixes". Of course, Big Brother can mess with your world, and has in the past, by introducing an error into the system. The error is not huge, measured in yards, but it can be there. The good ol' free market got around that error by introducing DGPS, or "differential", which corrected the government induced error. And today we have the latest and greatest, the Wide Area Augmentation System, or WAAS. WAAS incorporates ground stations and increases accuracy up to 5 times over standard GPS. Most new receivers you can purchase today are WAAS capable.
A simple hand held GPS unit is a good thing to have around, especially if you must travel the back roads when bugging out, or worse, if you're left on foot. As stated earlier, you shouldn't depend entirely on GPS, but it is a valuable tool to add to your gear. Nowadays they're pretty cheap too, you can get a Garmin hand held for less than 150 bucks. Having a second navigation tool is essential, especially if you become lost or disoriented. There have been cases where folks have become disoriented, and didn't believe what their compass was telling them, so having GPS to augment your compass is a good idea. It's hard to argue with what TWO devices are tellin' you! BUT (there's always a but, ain't there?), if the GPS is telling you one thing, and the compass another.... Go with the compass! North is north, and that's all a compass does is point north. Unless your standing next to a huge magnet or something..... But as I said, Big Brother can manipulate GPS. As far as I know, he hasn't found a way to manipulate polar north yet!
GPS can also be effected by other things, like ionospheric disturbances, solar flares, satellite orbit errors, etc. So treat it with a healthy dose of skepticism if you think it's telling you wrong, and double check it against a compass, maps, or whatever else you might have on hand. Your brain is your best navigation tool, but GPS sure can take a load off of it and free you up to do other things. So long as there are still 3 GPS satellites in operation overhead, and you have solar rechargeable batteries, GPS will remain a very valuable navigation tool. I've been using it on boats regularly since 1996, and I don't leave shore without it!