Barter-based economies are one of the earliest, predating monetary systems and even recorded history. People can successfully use barter in many almost any field. Informally, people often participate in barter and other reciprocal systems without really ever thinking about it as such -- for example, providing web design or tech support for a farmer or baker and receiving vegetables or baked goods in return. Strictly Internet-based exchanges are common as well, for example exchanging content creation for research.
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).
This sort of scenario was so undesirable that societies must have created money to facilitate trade, argues Smith. Aristotle had similar ideas, and they’re by now a fixture in just about every introductory economics textbook. “In simple, early economies, people engaged in barter,” reads one. (“The American Indian with a pony to dispose of had to wait until he met another Indian who wanted a pony and at the same time was able and willing to give for it a blanket or other commodity that he himself desired,” read an earlier one.)
Since the 1830s, direct barter in western market economies has been aided by exchanges which frequently utilize alternative currencies based on the labor theory of value, and designed to prevent profit taking by intermediators. Examples include the Owenite socialists, the Cincinnati Time store, and more recently Ithaca HOURS (Time banking) and the LETS system.