Commuting on an internally-geared bike, if I get a small puncture I'll patch the tube with the wheel still on the bike. (Usually only takes a couple of minutes to find, patch, and get the tire back on, a bit faster than removing a nutted-axle internally-geared hub.)

But I carry a spare tube for larger gashes that don't patch well.

On my touring bike I usually carry both 700C and 26" tubes -- if the person I'm riding with has a flat, that slows me down as much as it does them. (But then, on my touring bike I also carry a chain whip, crank puller, BB tools...)