I have never bothered to turn the camera off when switching lenses.
If I ever had any problems like a lens not working properly, it would easily have been fixed by turning the camera off and on again, and it can't have happened many times because I can't recall any incident. Besides, that could just as well have happened if I turned the camera off for switching the lens.
As Matt Grum pointed out that he couldn't find any instruction to turn the camera off in the manual, I checked the camera manuals for my EOS 300 and my EOS 5D mark II, and the procedure for attaching a lens doesn't even mention turning off the camera. I checked the manual for a lens also, and that doesn't mention it either.
I definitely remember reading it somewhere, so it might be there in some manuals, but if there was a good reason for turning the camera off, it would be in every manual, both for cameras and lenses, and it would be hard to miss.