How much validity do you give to anonymous sources?

How much validity do you give anonymous sources when you are watching a news show or reading a magazine like Time or Newsweek, etc.? If something is said about a case or current event but it is said by an anonymous source because they were not authorized to speak to the press, or they fear reprisal from the group they are with or speaking against, how much do you trust it? If one can hardly believe anyone online when they have a name, even if it is just a user name, how can one more believe something from someone with no name?