I got a handheld Garmin eMap (now obsolete) eleven years ago in lieu of a cyclometer and would never go back (although I can see some sense in having both). Accuracy in general is very good and when comparing distances on club rides I find that my numbers are almost always somewhere in the middle of those recorded by folks with cyclometers. There are occasional glitches, especially in the urban canyons of city centers where the buildings hide much of the sky and also create reflected satellite signals, and also in dense redwood forests where the unit will lose satellite contact periodically. That can reduce the recorded mileage slightly, but it's very rare that the discrepancy is significant. OTOH, the max. speed reading can be thrown way off by a single false reading and I do sometimes get clearly spurious values for this.

But the benefits are numerous - being able to see at all times where you are on the map, what alternate routes will get you back if you're getting tired or running out of time, keeping records of where you went, how fast you were, etc. I also upload many of my rides and associated pictures to the everytrail.com site, such as this one from yesterday:
http://www.everytrail.com/view_trip.php?trip_id=429752
[the site looks at the time stamps on the GPS tracklog and compares to the times embedded in the picture files to determine where each photo was taken]

The GPS is especially handy while touring since the maps contain the locations of millions of businesses. Being able to find the location of the next grocery store, bike shop, library, or emergency motel has come in very handy at various times.