I'm surprised Tom didn't mention Ventana Canyon's Canyon course in Tucson with the "map" with instructions on how to get from the 9th green to the 10th tee. If I remember correctly, its over a mile. It sure looks like they built the Mountain Course first then decided they had some land on each side of it so they put the front nine of the canyon on one side and the back nine on the other. There are some pretty good individual holes, but the routing is really choppy.
The strangest routing I've seen though has to go to Ironbridge GC near Glenwood Springs, Colorado. The first hole starts off relatively close to the clubhouse, then you take about a 1/2 mile ride through a neighborhood to #2-8 which are generally close together, then back along the same path to #9 which is a short par three that finishes on the other side of the driving range from the clubhouse.
The fun is only beginning, however, as you take a 1 mile ride up a canyon to reach #10 tee and play four holes of mountain golf before heading back down the same path, then turn right and go for a bit to #14, cross a road to get to #16, and return to the clubhouse at #18. I don't know how much walking would be required to play the entire course, but its not for anyone but avid hikers and would have to be a 5+ hour undertaking if one wanted to actually play golf too.
All that said, its got some pretty cool holes and spectacular views. I think the four hole mountain stretch would seem strangely out of place except that the entire course is choppy so in a twisted way that makes it more logical to go way up the mountain to play a few holes before coming back down. I'm not sure how popular this has been, however, since the course is now advertising for public play on their website.
Here's a link to the routing and hole descriptions:
http://www.ironbridgeclub.com/golf/thecourse.php