The term Anti-copyright describes both the opposition to copyright law and specific statements that are added to works in order to encourage wide distribution.
Anti-copyright notices
Such statements are legally required because, in international copyright law, works are protected even if no copyright statement is attached to them. However, "anti-copyright" statements typically do not take the form of either sophisticated open content licenses or a simple dedication to the public domain; instead, they usually just encourage wide distribution.
An example of an anti-copyright notice is the following: "Anti-Copyright! Reprint freely, in any manner desired, even without naming the source." Where such notices are attached depends highly on the type of work. They are often found in anarchist magazines and books.
Most people would regard such "anti-copyright" notices as being equivalent to a dedication of material into the public domain, however, they are less accurate and need to be interpreted individually. For example, if just the distribution is encouraged, modification is still illegal, making the material ineligible for collaborative writing projects like Wikipedia.
Anti-copyright movement
The opposition to copyright law per se is not strictly limited to anarchists. The term "infoanarchism" was coined in recent years (starting with a July 2000 TIME Magazine article about Ian Clarke called "The Infoanarchist") to describe specific opposition to intellectual property, often including patents.
The classical anarchist perspective on anti-copyright is that ideas and knowledge should not be owned or controlled. This is perhaps best summed up in Pierre-Joseph Proudhon's slogan Property is Theft. Anarchists do not consider plagiarism and theft of other people's ideas a good thing. Anarchists and others who do so would be looked at as dishonest and untrustworthy. What is more important to anarchists is the refusal to "own" ideas and knowledge.