Every time I sell a bike, I include a tube and a set of tire levers. Until that point, most folks aren't even aware that flats happen. One woman I talked to told me she just walked to the nearest road (from the mup) and flagged down a ride. Multiple times.
I, of course, carry the kitchen sink. I have an entire bag dedicated to tubes, folding tire, patches, glue, tire guage. The other bag carries the tools, including a chain tool and a faux leatherman. It's nice to have those needlenose. The handlebar bag carries the sandwiches, street shorts, sunscreen, etc. I need to get a rack or two for that bike.