As others have noted, all 3 (map, compass, and GPS) are just tools. Each can fail, or be lost, etc. And each tells you something different. All integrate together well.
I use a mapping GPS. If I want, I can plot out my intended route and enter it into the GPS beforehand. Or, since it already has the appropriate maps in it for my usual hiking areas, just do no preparation and see my current location and my track plotted on a topo while hiking.
Sometimes I carry it in a pouch attached to my pack shoulder strap which allows me to pop it out at any time and see at a glance where I am. In adition, if I have an active route or an active "goto" on a waypoint I can see how far and what direction to the next waypoint. (Just did a battery life test on my 60CS last night: 14hrs continous operation using possibly less-than-fully-charged 1600MAh NiMH batteries, so I should be able to get 20hrs or so out of 2200+ MAh batteries or lithiums.)
Sometimes, I just throw the GPS in my pack and only get a fix if I need it. This would allow one to get weeks of battery life if needed. A bushwacker using map & compass might do this as a backup. ([Technical] climbers might call this "carrying one's security in one's rucksack".
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Another mode would be to carry the GPS in the top of one's pack turned on to record a track so that one can see where one has been after one gets home. This works best if you can load the track into a computer and view it on the large screen plotted on a topo.
2 examples of actual use:
1. Last March, I did a solo Isolation bushwack.
http://www.vftt.org/forums/showpost.php?p=63014&postcount=68 . Following a route description, I put waypoints at the turns and connected them into a route and loaded it into my GPS. I also printed out a nice 1:25K scale topo to augment my AMC guidebook topo map. I used the GPS to verify each waypoint as I arrived plus an occasional check along each leg of the bushwack. I also waypointed the stream crossing. I put each leg heading into my compass and used that to guide me between waypoints. (Spider Solo was a few hours a head of me and while I followed his tracks much of the way, I navigated as if there were no tracks. On the way back I broke away from his path for a good bit and followed a compass heading back to the stream crossing. The GPS conviently gave me the heading to the waypoint I had recorded on the way in.)
2. I was doing a long solo BC XC ski. I was 12 mi from the car (at Lincoln Wds) when the sun set (junction of Shoal Pnd Tr and Ethan Pnd Tr) and it was a dark overcast night (new moon). I had been on parts, but not all of the trail before. I had the route programmed into the GPS and used it to keep track of where I was as I skied back to the car. I was able to follow the trail by visual means, but there was one wide open spot which I used prior knowledge to get though. (It might have been difficult or at least taken some time to find the continuation of the route without that prior knowledge--it wasn't obvious as I passed through the opening.)
In both of these cases, I probably would have been ok without the GPS, but it was comforting to have the backup.
Doug