I would definitely carry a spare tire if possible, especially if you're using tires that are in any way unusual. On my last tour, I was riding 650b tires (which was, obviously, a pretty dumb thing to do). The odds of getting a suitable replacement tire at a bike shop were poor. But my tires were new, and I had a spare, so I figured it wouldn't be a problem. Well, my front tire blew out on the last day of the tour; sidewall separated from the bead and went BLAMMO. Lucky me, I wasn't on the bie at the time (but had been cruising down a hill at 35 mph just a few minutes earlier). Tire was instantly totaled. I mounted the spare, and we were on our way no problem. I replaced the tube, of course, but I was able to patch the tube that blew. I don't see the need for more than two spare tubes; they are easy to patch.
Out on a leisure ride this last Sunday, I rode over some glass and shredded my rear tire. Classic bad luck, I was already 60 miles from home, literally turning around to head back, when it happened. I booted one gash with a dollar bill, booted another gash with the wrapper from a Clif bar, and not many miles later was lucky enough to find a bike shop where I replaced the tire (4 PM Sunday; how's that for luck?
). The replacement tire is junk (expensive junk) but they had something, I didn't have to call my wife to come pick me up, so I was happy.