The Owenite socialists in Britain and the United States in the 1830s were the first to attempt to organize barter exchanges. Owenism developed a "theory of equitable exchange" as a critique of the exploitative wage relationship between capitalist and labourer, by which all profit accrued to the capitalist. To counteract the uneven playing field between employers and employed, they proposed "schemes of labour notes based on labour time, thus institutionalizing Owen's demand that human labour, not money, be made the standard of value." This alternate currency eliminated price variability between markets, as well as the role of merchants who bought low and sold high. The system arose in a period where paper currency was an innovation. Paper currency was an IOU circulated by a bank (a promise to pay, not a payment in itself). Both merchants and an unstable paper currency created difficulties for direct producers.
The history of bartering dates all the way back to 6000 BC. Introduced by Mesopotamia tribes, bartering was adopted by Phoenicians. Phoenicians bartered goods to those located in various other cities across oceans. Babylonian's also developed an improved bartering system. Goods were exchanged for food, tea, weapons, and spices. At times, human skulls were used as well. Salt was another popular item exchanged. Salt was so valuable that Roman soldiers' salaries were paid with it. In the Middle Ages, Europeans traveled around the globe to barter crafts and furs in exchange for silks and perfumes. Colonial Americans exchanged musket balls, deer skins, and wheat. When money was invented, bartering did not end, it become more organized.
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).
Check online swap markets and online auctions that have a bartering component such as Craigslist.com (check under "For Sale" for the Bartering category), Swapace.com, SwapThing.com, Barterquest.com, U-Exchange.com, Trashbank.com and Ourswaps.com. Check for local bartering clubs. Your local Chamber of Commerce may be able to provide you with information on similar clubs in your area.