Some people may not be able or willing to save money, but wish to see the World anyhow. It is possible to travel with very little or even no money at all.
This means either keeping expenses low, or having earnings while one travels.
If you have more time than money available, you will find out that walking or cycling is possibly the best way to discover a new place.
This can be combined with hitchhiking, which is faster and normally just as cheap.
Normally it is illegal to use public transport without paying, although some places are experimenting with free public transport (such as Hasselt in Belgium and Portland (Oregon)). In some countries or cities it can be worth a try to use the public transport without paying - on the risk of being fined. It is best to ask locals who have experience using public transport without paying.
The objective of hospitality exchange networks is to meeting new, and local, people. But besides that it's a fun and easy way to get acquainted with an area or city it can also be a way to get a cheap or even free place to stay the night.
Budget travellers usually buy their food in markets or supermarkets. In country with peculiarly high hygiene standards, you may be able to find perfectly acceptable food in supermarket's rubbish.
In some cities there are very cheap restaurants, such as Berlin's Volkskuechens. Some countries also have heavily subsidised university restaurants sometimes open to foreign students as well. Germany for instance has Mensas, offering famously tasteless meals for 2-3 euros.
Many art galleries, museums and other attractions have discounted or free days at least once a month. Tourist information offices will sometimes be able to tell you about these.
The most straightforward way to earning money on the road is obviously to find some work.
This is more easily done through contacts, and as a matter of fact hitchhiking may come very handy here. Contacting expatriates may also provide for opportunity.
Obvious jobs for travellers include harvesting, teaching English and waiting at restaurants or bars in touristic areas.
Resources exist, such as Susan Griffith's biennial Work your Way around the World published by Vacation Work.