When somebody hands me their camera, I generally change it to aperture priority, the mode that I generally use. The camera's usually on full auto mode, which doesn't give me the results that I'm looking for.
I was thinking about this a few days ago when somebody handed me their D3000 to take a picture of them. I knew that I would've gotten an underexposed subject and a properly exposed background if I left it on auto, so I tried switching it to aperture priority to lower the shutter speed and pop up the flash. I has a bit of trouble selecting the aperture as I wasn't familiar with the D3000's layout, but I got the image after all. However, I forgot to change the camera back to full auto when I handed the camera back to them.

Oops...
Of course, that's generally only the case with Nikons. I don't know how to use Canons very well (I know the general layout for a few of their bodies, but otherwise I don't really know what does what), but I like to leave it on full auto with the Canon DSLRs.
The worst part about taking a picture with somebody's DSLR is when their eyes are totally different than yours. I wear glasses, so generally I have trouble composing for people without them as their viewfinder is so out of focus. I could always change it with the diopter adjustment, but I'd need to change it back and it's difficult to find exactly where it was.