Economists since the times of Adam Smith (1723-1790), looking at non-specific pre-modern societies as examples, have used the inefficiency of barter to explain the emergence of money, of "the" economy, and hence of the discipline of economics itself. However, ethnographic studies have shown that no present or past society has used barter without any other medium of exchange or measurement, nor have anthropologists found evidence that money emerged from barter, instead finding that gift-giving (credit extended on a personal basis with an inter-personal balance maintained over the long term) was the most usual means of exchange of goods and services.
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.
Companies may want to barter their products for other products because they do not have the credit or cash to buy those goods. It is an efficient way to trade because the risks of foreign exchange are eliminated. The most common contemporary example of business-to-business barter transactions is an exchange of advertising time or space; it is typical for smaller firms to trade the rights to advertise on each others' business spaces. Bartering also occurs among companies and individuals. For example, an accounting firm can provide an accounting report for an electrician in exchange for having its offices rewired by the electrician.
When two people each have items the other wants, both people can determine the values of the items and provide the amount that results in an optimal allocation of resources. Therefore, if an individual has 20 pounds of rice that he values at $10, he can exchange it with another individual who needs rice and who has something that the individual wants that's valued at $10. A person can also exchange an item for something that the individual does not need because there is a ready market to dispose of that item.
Business to consumer barter may include things like free merchandise for a customer who is willing to provide sales leads. Person to person barter can include almost anything you can imagine. Auction sites are a good place to find others willing to trade for things you have. Classified ads, online or in print, are another handy way of conducting barter transactions, and so are barter clubs.