OpenJK - Community effort to maintain and improve Jedi Academy and Jedi Outcast by Raven Software.
MafiaUnity - Open-source Mafia game framework.
donut - Reimplementation of The Simpsons: Hit & Run in modern C++ and modern OpenGL.
Carnage3D - Reimplementation of Grand Theft Auto.
etc.), take a look at Open Source Game Clones. If you are also interested in clones and similar games (0 A.D. Actively maintained open-source game remakes.