Gift economy is a system based around getting people what they need (and want), without the use of money. Instead of a bartering system, where 10 eggs could buy you a kilo of flour, the idea is to give freely to everyone and anyone, and others will do the same for you, so that no one is left out. When and if you need something, just ask, and it will be provided. In turn, you give what you can to the next person who needs it. No money is exchanged, but the gift of goods flows to everybody.
Critics state that "gift economy" may be a disguised form of barter- or quid-pro-quo-economy ("okay, have some eggs, but I will ask you to fix my roof") or aim to accumulate reputation, alas "buy" a high up place by "giving" tactically.
Gift economy may work after global wealth redistribution.
As it's much easier to give away stuff you got for free, dumpster diving is a good starting point for gift economy systems.
Here is an interesting story, of a man from India, who runs his auto-rickshaw on principles of gift-economy and 'Pay-it-forward' ethic: http://mammovies.com/blogs/2011/06/18/uday-bhais-diary.
See also: Sharewiki