Trading goods and services without the use of money is called bartering. Early civilizations relied on this kind of exchange. Even cultures in modern society rely on it. Think of people in prison who commonly trade cigarettes for protection or extra food. For the most part, they don't have cash. So, like people in pre-currency economies, they work with what they have.
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.