If you have the right gear and aren't afraid of the outdoors, bicycling is one of the cheapest travel methods there is for short-to-medium distances. Obviously, you don't have to pay for gas or a ticket, and maintenance costs for a properly maintained vehicle are minimal. Not all bicycles are suited for long-distance travel, however, and there are limited options in terms of safe bike trails, so be sure to plan your route ahead of time.
In states where it is legal, hitchhiking is the classic cheap travel method. Of course, it also comes with serious risks, especially for female travelers. If you can't find a friend to hitch a ride with, be sure to study the local traditions and dialect of the major cities and towns en route to your destination and pay attention to how your clothing and mannerisms will appear to a potential ride.
Boon-docking is the practice of living out of your vehicle while traveling. If you have an RV, then this is hardly a scary prospect, but people with cars of all makes and models can get away with boon-docking if they know a few tricks (see Resources). The money saved that would have been spent on lodging adds up for long trips.
If you want to travel long distances on the cheap, your best bet is usually taking the bus or the train. Although it may be slower and less luxurious, the price per mile is usually significantly cheaper than the equivalent for an airline ticket or paying for gas and a tune-up for your car.
As with hitchhiking, couchsurfing -- staying overnight at a stranger's house -- involves more personal risks than traditional travel methods, but you can now find vetted and verified hosts on the Internet to reduce the risk. Couchsurfing websites help you find a community of thrifty travelers and hosts (complete with references) so you can learn more about the person with whom you'll be staying. Be sure to learn the host's guidelines and expectations before finalizing plans. As always, use common sense. Couchsurfing is not recommended, and included in this article for purposes of discussion only.