Some do, and some don't. Some carry a patch kit instead of or in addition to a tube. If you want to be self-sufficient, being prepared to change a flat is a must. Also a pump or other source of air. But there are other steps you can take to minimize the risk like heavy duty tires or tire liners. For me, my commute keeps me fairly close to the bus route. I try to keep supplies with me, but it doesn't always happen, and I don't worry too much about it. But when traveling outside of bus hours, I make an extra effort to remember or run the risk of a long walk home.

It's hard to remember the last flat tire I got since switching to tougher tires, but the aggravation you can save by being prepared for a flat can far outweigh the annoyance of carrying extra supplies.