There are industries in which cooperatives have a very significant share of the U.S. economy, especially in rural areas, although not always worker cooperatives.
During the U.S. Great Depression, many cooperatives were established to provide rural electric service, to provide banking (a customer owned banking cooperative is called a credit union), to market and sell crops, and to sell farm supplies. This encompasses both producer and consumer cooperatives, although the member farm businesses are typically self-employed business people rather than employees.
Many insurance companies are organized as mutual companies owned by their insureds, which are a form of cooperative (e.g. Mutual Of Omaha, Northwest Mutual, and Amica). Professional malpractice insurance firms and health insurance firms have historically often been organized as mutual companies.
Homeowner's associations are resident owned, as are a variant on that theme called co-operative apartments.
College bookstores are frequently consumer cooperatives.
Many colleges have co-operative housing in which the housing and dining services is owned by the co-operative which is controlled by people who are both the predominant consumer of its housing and dining services, and the predominant employees of the co-operative. University of California - Berkley, University of Michigan - Ann Arbor, and Oberlin College all have large cooperative housing systems.
Some colleges, while officially organized as non-profits, are de facto faculty controlled and owned.
In the Pacific Northwest, the plywood industry is largely organized in the form of worker cooperatives.
Taxi companies in many cities are typically employee owned.
Law firms and accounting firms (and historically, until about a decade before the financial crisis, investment banks) are professional employee owned. So are medical practices. The New York Stock Exchange is a cooperative controlled by member brokers who work in the stock exchange.
The leading academic survey of cooperative ownership and its alternatives is "The Ownership of Enterprise" (1996) by Henry Hansmann.
Are worker cooperatives socialist, capitalist, or their own category?
A system in which worker cooperatives were the predominant form of firm organization in a country would be called "Communist". The whole point and organizing principle of communism is to replace firms owned by owners of capital with firms owned by workers. But many democratic socialist and capitalist countries have worker cooperatives in particular niches where this form of organization works well.