As Orlove noted, barter may occur in commercial economies, usually during periods of monetary crisis. During such a crisis, currency may be in short supply, or highly devalued through hyperinflation. In such cases, money ceases to be the universal medium of exchange or standard of value. Money may be in such short supply that it becomes an item of barter itself rather than the means of exchange. Barter may also occur when people cannot afford to keep money (as when hyperinflation quickly devalues it).
Adam Smith, the father of modern economics, sought to demonstrate that markets (and economies) pre-existed the state, and hence should be free of government regulation. He argued (against conventional wisdom) that money was not the creation of governments. Markets emerged, in his view, out of the division of labour, by which individuals began to specialize in specific crafts and hence had to depend on others for subsistence goods. These goods were first exchanged by barter. Specialization depended on trade, but was hindered by the "double coincidence of wants" which barter requires, i.e., for the exchange to occur, each participant must want what the other has. To complete this hypothetical history, craftsmen would stockpile one particular good, be it salt or metal, that they thought no one would refuse. This is the origin of money according to Smith. Money, as a universally desired medium of exchange, allows each half of the transaction to be separated.
It’s hard to answer that without actually seeing a modern gift economy in action. Luckily, modern gift economies actually do exist. On a small scale, they exist among friends, who might lend each other a vacuum or a cup of flour. There’s even an example of a gift economy on a much larger scale, albeit one that’s not always in operation: The Rainbow Gathering, an annual festival in which about 10,000 people gather for a month in the woods (it rotates among various national forests around the country each year) and agree not to bring any money. Groups of attendees set up “kitchens,” in which they prepare and serve food for thousands of people every day, all for free. Classical economists might guess that people would take advantage of such a system, but, sure enough, everyone is fed, and the people who don’t cook play music, set up trails, teach classes, gather firewood, and perform in plays, among other things.