There are 17 games to choose from - games in the top 50 (of active games going) on the site, which has not had a team tournament start within the last year - and does not have a current team tournament running.
Some interesting notes: [the (###) is the rank of "popular" on active game list]
International Checkers (#47) - Only game on list which has NOT had a site team tournament yet.
Halma 8x8 (#44) - Hasn't had a TT since December 2004
Chinese Chess (#45), PahTum (#29), and Loop Chess (#41) - not since 2005
Massacre Chess (#34) is the most recent in the list, having one start July 2009
Five in Line (#13), Plakoto (#15), and Froglet (#16) are the 3 most "popular" games in the list - with last TT June 09, May 08, and Nov 08 respectively.