You're a miles from anywhere and you get a flat tire on your bicycle. The glue in your patch kit is dried out, you're out of CO2 cartridges, and you don't have a spare tube. What do you do?
The usual recommended solution is to stuff your tire with dry grass and leaves. I've never had to do that personally, but people who have done it tell me it can work well enough to keep from damaging the rim, though shoving the tire onto a grass stuffed rim can be a challenge.
I have tried this solution offered on Life Hacker, which is to tie the leaky area off with some string. I wasn't able to make that trick work, but Your Mileage May Vary and if you're desperate it doesn't hurt to try.
You should avoid riding on a flat tire. You can damage your rim -- if you flat it's likely the rear tire and the wheel is generally the second most expensive part of your bike after the frame. Your tire will also easily roll off of the rim, causing you to lose control even at slow speeds.