Many websites are a mixture of types. For example, a business web site may promote the businesses products, but may also host informative documents, such as white papers or provide news for it's visitors. Remember, information is the soul of the internet and if used wisely articles and informational pieces are a good hook to bring in visitors.
There are also numerous sub-categories to the ones listed above. For example, a fan site may be a vanity site on which the administrator is paying homage to a celebrity. Another example would be a hobby site where the webmaster shares their knowledge with other like minded individuals and through forums or chat rooms creates a dialogue with them.