While I have managed to make it from Woodland Park back home to Thornton at the time with 4 plugs in my sidewall and stopping to air the tire back up twice along the way, I like having a spare with me.
I like the idea of laying it down in the back because it keeps the weight down and doesn't limit visibility like your typical rear mounted tire carrier does. However, I also like having cargo room. My original idea for laying it down in the back was to put a small air tank right behind the seat, and then the spare right behind that. It would stick out a little more than Proracedriver's, but probably not too much more. Then put a rack across the top just above the spare to still be able to sit a cooler, camp boxes, etc on top of. On either side of the spare I figured there should be just enough room to fit some fluid holders and my tool bags. Under the back seat is where I typically like to store spare shafts and u-joints.
If I went rear carrier I would design it to be easily removed, that way if I'm out in Moab or somewhere and don't want to risk dragging it all over the place I can take it off and leave it at base camp. I'm still undecided how I want to go about it, and luckily for now the 31" spare fits just fine inside. I won't have to make a final decision until this winter at the earliest.