There are lots of those. Super Sprint, Ironman Offroad, Jupiter Masterdrive, Bubble Bobble, Ballerburg, Gauntlet II and naturally many sport (e.g. football), fight (e.g. snowball) & board games. Board games are naturally turn based.
If you're interested about source code for some 2-player games, see the turn-based "Ballerburg" and "ST-concentration" games here: http://koti.mbnet.fi/tammat/hatari/programs.shtml
If you're on Debian based Linux system, here are few tiny 2-player games packaged into Debian packages: http://koti.mbnet.fi/tammat/hatari/games.shtml#2player
(Because packages were made for Nokia's Maemo Linux, .desktop files for the games are in usr/share/applications/hildon/ directory. Copy them e.g. into your ~/Desktop/ directory if you want to run those games directly by clicking on their .desktop file.)