In Moab I always kept my spare on the trailer and carried a plug kit with me.
On the long distance stuff I do, I always carry a spare in the rear cargo area (35"). I would NEVER put it on the roof for the following reasons (especially for hard trails--I can at least see an argument for an overland type expedition rig)
1: increase in COG
2: looks stupid
3: increase in COG
4: hard to get up/down
5: looks dumb
6: increase in COG
7: mileage (but for a trailer queen it probably doesn't matter)
7: increase in COG
8: in full bodied/cageless rigs it becomes dangerous in a roll over.
and it also looks retarded. I would probably put a chrome stinger on my rig before I would put a tire on the roof.
some rear mounted carriers interfere with departure angle and do restrict visability (although, not quite as bad as being upside down. I always had a hard time seeing what was behind me while hanging from my harnesses). If you're running 38's then I would probaly carry a good plug kit and air for day trips. If you're using your rig to get 100 miles away from civilization, then definately look into a way to carry a spare.