When a company is monopolized free enterprise is destroyed, that industry's product prices are reduced, business generally prospers and consumers generally don't.

A monopolistic company is any company that has no competition at all, and has the sole right to sell a product.

It has two distinct definitions:
No close substitutes: A monopoly is not merely the state of having control over a product; it also means that there is no real alternative to the monopolized product.

A price maker: Because a single firm controls the total supply in a pure monopoly, it is able to exert a significant degree of control over the price by changing the quantity supplied.

Examples of (historical and current) alleged and legal monopolies
The salt commission, a legal monopoly in China formed in 1758.
British East India Company; created as a legal trading monopoly in 1600.
Dutch East India Company; created as a legal trading monopoly in 1602.
U.S. Steel; anti-trust prosecution failed in 1911.
Standard Oil; broken up in 1911.
National Football League; survived anti-trust lawsuit in the 1960s, convicted of being an illegal monopoly in the 1980s.
Major League Baseball; survived U.S. anti-trust litigation in 1922, though its special status is still in dispute as of 2008.
United Aircraft and Transport Corporation; aircraft manufacturer holding company forced to divest itself of airlines in 1934.
American Telephone & Telegraph; telecommunications giant broken up in 1982.
Microsoft; settled anti-trust litigation in the U.S. in 2001; fined by the European Commission in 2004, which was upheld for the most part by the Court of First Instance of the European Communities in 2007. The fine was 1.35 Billion USD in 2008 for incompliance with the 2004 rule.
De Beers; settled charges of price fixing in the diamond trade in the 2000s.
Apple Inc., Accused of forming a Vertical Monopoly, with iPod, iTunes, iTunes Store, and the Fair Play DRM System.