Shamus tried to create a definition. Spurred by his attempt, I did too. My version tries to separate geeks from people who enjoy non-geeky intellectual amusements (i.e., many theologians and philosophers) and those who partake in solitary intellectual entertainments (i.e., people who have read or seen The Princess Bride but never quoted it in conversation).
geek (n):Anyone else have a definition of geek?
A person who entertains himself/herself primarily through the communal creation of or participation in one or more fictional settings. The settings used may be intended for future reality (i.e., settings of inventors, programmers, etc.) or may simply be established for amusement (i.e, settings of gamers, anime fans, etc.). The community of direct interactions may be small (two people playing a game whose setting was established by a wider community) or large (all the programmers who contribute to Linux).