Database (MySQL):
As indicated, an Add On/Option such as a CMS, E-commerce or Forum include a database, so there would normally be no need to purchase an extra one.
Occasionally, in circumstances where a site does not make use of those products, but where the site offers its visitors a wide choice of content options, e.g. a photo gallery, the best way of storing the content is in a database. In that way, the site remains efficient, only downloading content as it is selected by a visitor.