CryEngine is considered to be one of most sophisticated commercial game engines available today with games like Far Cry, Crysis and Crysis 2 based on it.
Many new games based on latest CryEngine 3 are coming in future including MechWarrior Online and Star Citizen.
Star Citizen is a space adventure and exploration game by Chris Robert, creator of Wing Commander series. He recently did a 'Ask Me Anything' session on Reddit where he hinted that CryEngine 3 may be coming to Linux.
It depends on Crytek and having the engine support OpenGL as well as DirectX. There may be some good news in the near future as we've discussed it with Crytek and they themselves want to address this.
Another comment by him:
The server side of CryEngine can run on Linux. Unfortunately the client side currently does not and is tied to DirectX. We've been discussing OpenGL with them for Linux and Mac reasons and they have some other licenses that also want to do it, so it may happen in the near future.
Star Citizens developers have now started a poll where you can vote for Linux support. If they feel that there is strong demand for Linux, they may talk to Crytek about it.
Unity and Source engine have already confirmed Linux support. If CryEngine 3 adds Linux support as well then Linux as a gaming platform will get a major push in coming years.