I suspect that the reason for the phrasing (in the documentation for Classify) "Examples of built-in classifier functions include" is that this is a continually updated set and is updated through the connection to the Wolfram Server (just as things like CountryData are). But it would be very nice if there were a place where one could see the full current list. For example via a special function call such as

Classify["Examples"]

and a list of properties for any particular case via something like

Classify["NameAge" ,"Properties"]