I've noticed that many people have had problems with Cedega only running Far Cry once before it needs to be re-installed. After a whole afternoon of fiddling with md5sums and cached shaders, I came across the solution: Don't use Cedega. Use regular Wine.
1. Download the latest Wine release (071604) and install it.
2. Install Far Cry with an installer from here: http://liflg.sourceforge.net
3. Go to /the/directory/where/farcry/is/Bin32, and run wine FarCry.exe
There are some texture discolorations, and you might need to use some cheats to get to the next level (sometimes it doesn't work), but other then that, it works pretty well. Hope I've helped !

PS: Don't worry about Wine not running it because it uses Direct3D9. The installer automatically sets the configuration file to use the OpenGL renderer, which works fine under Wine.
At the end of the Carrier level, when you retrieve the boat, the level doesn't fade out properly. To circumvent this and get to the Fort level, start the game like this:
wine "FarCry.exe" -- -devmode
You can then pick the level you want to start at (don't cheat ).

By the way, tell me if it works or not! If it doesn't, say so, and I'll take a look.