Ecere Chess is a very simple, but fun 3D chess game with AI and network support. It will run on any platform supported by the Ecere SDK (currently Windows and Linux). It is a good opponent with whom to practice your chess skills, as although it is not very smart, it will rapidly take advantage of your mistakes since it sees all possibilities two moves ahead.
SoapQuest1024 is a small written after reading "20 Open World Games" on Gamasutra and coming across "Adventure". It's a very simple tile-based game written in 1024 lines of Java. You can wander around the place, picking things up and using them on other things by walking into them. You can save the gameand go back to it later. It's fully data-driven, based on a simple CSV format, and has things like wandering treants and a day/night cycle with light calculations.