An OGame clone is a game that shares similarities with OGame (either in terms of gameplay, aestethic, or even as a general game idea). It is most often made by other publishers, unrelated to Gameforge. These games are hosted on private servers, where you can also find Clone builders, the most famous one is XG Proyect where all the other clones are based from, like 2Moons, XOrbit or Galaxy of Masters. The package is distributed for free. It is OpenSource and is based on PHP and MySQL or .NET and MYSQL.
A list of OGame clones can be found at gametoor.com