Draughts (checkers) and chess games are very popular, also go board game is becoming more and more popular, so It's wise to include these board games into distribution.

- Chess game could be glchess ( version http://prdownloads.sourceforge.net/glchess/glchess_1.0RC2-1dapper_all.deb?download or higher, will be included into GNOME Games ver 2.18, see http://live.gnome.org/GnomeGames ) or pychess (http://code.google.com/p/pychess/ ). Pychess has ability to choose easier/harder levels, this is very important for beginners (it seems glchess will also have this in future), while glchess is nicer look and even optional 3D look, when  python2.4-gtkglext1 (from http://prdownloads.sourceforge.net/glchess/python2.4-gtkglext1_1.1.0-1_i386.deb?download ) and python-opengl packages are installed. Note, that on Ubuntu 6.06 (dapper) glChess crashes in 3D View, see http://sourceforge.net/tracker/index.php?func=detail&atid=106348&aid=1594072&group_id=6348
Also it would be nice to use cool 3D chess figures like http://brutalchess.sourceforge.net has.

- For draughts(checkers) game I didn't found any separate game, only gtkboard (nice project, but not developed since 2003-10), ggz-gtk-games, ggz-kde-games,  includes checker and chess games in Ubuntu/Debian.

- Go board game could be GnomeGo (http://se-linux.inso.tuwien.ac.at/se2wiki/GnomeGo - tested ver. 0.5 deb package ) or Quarry - a multi-purpose GUI for several board games, at present Go, Amazons and Reversi (a.k.a. Othello.) Quarry allows users to play against computer players (third-party programs, e.g. GNU Go or GRhino) or other humans, view and edit game records. Playing on Internet game servers will be supported on ver. 0.3.
Also there is cgoban (has internet play ability) and gtkgo packages, but it seems development of gtkgo is stoppet 4 years ago :(