In order to describe a market, both the participants and goods available for exchange must be defined.  These two definitions form the scope of a market.  In this manner, the environment of trade can be partitioned or subdivided by utilizing subsets of the total possible participants and goods, services, or information. 

The most common partitioning scheme is the subdivision of markets by country, as national law establishes a clear distinction between various subsets of participants and goods.   In such an example, the components number in the millions and the sheer magnitude of variables and interactions appears almost impossible to analyze.   However, this is only an abstraction.  The market could have been partitioned in any number of ways―either by expanding the scope to a global, galaxial, or universal markets, or by further restricting the scope to states, cities, and localities. Likewise, the scope of the market can be defined to include only certain subset of goods, services, or information.  Continuing in this vein, one arrives at the most basic market―the action of trade between a single buyer and a single seller exchanging a single item.

Thus, to answer the question of whether free markets exist, the proper scope need be attributed to the analysis.  By separating the environment of trade into its constituent parts, it is possible to find examples of free markets at various levels of abstraction.

For the simplest market, a single buyer and a single seller exchanging a single commodity, an example would be a teenager's weekly allowance in exchange for mowing the lawn.  For a local market, an example would be a neighborhood garage sale.  In both cases, all parties voluntary exchange goods or services in the absence of coercion or physical force, even if the parent is persuasive or the neighbor a convincing salesperson.  At the national level, citizens of a country are free to trade paper currency for hard currency and vice versa.  At the global level, language is arguable the most sucessfuly free market in human history: citizens of the world are free to voluntarily exchange information, ideas, alphabets, and the definitions of words which form language itself.

Furthermore, as the environment of trade is the sum action of its the individiuals and goods which participate in trade, each exchange forms a sort of sub-market in and of itself.   Any such sub-markets which exist in the absence of  physical force, compulsion, or coercion can properly be labeled a free market.  Despite complicated (and often regulated) supply chains, as all transactions ultimately end at an individual consumer, the majority of worldwide exchange takes place in such sub-markets.  

Thus, free markets not only exist, they are prevalent in modern economies.