Here is what a producer at Crytek said about the requirements in another thread:
'1.What are the minimum and recommended specs for Far Cry
Minimum: P-800, 256 RAM, GForce 3 or similar. This is what is necessary to play the game with some of the graphics options set to lower settings.
Recommended: P1.5, 512 RAM, GForce 4 or similar. This is what is necessary to play the game with all of the graphics options turned to normal levels.
The visuals are scaleable to get a reasonable framerate on the minimum spec machine. Additionally, the graphics can be set to an even higher level taking full advantage of more massive machines and the high-end graphics cards.
Also, we run on the ATI cards - in fact, anything that is fully DX9 compliant.
2.What sort of graphics card are we looking at to get good quality and performance?
We are working with both NVidia and ATI to ensure that we offer the best possible support for both card manufacturers and yes; we absolutely smoke on the upper end cards.'
I meet everything at reccomended except I only have a GeForce 3. I'm not sure if it is really worth upgrading. We'll see how it runs on a demo, however: I could always turn a couple of settings down. The game is beautiful, a couple dropped settings shouldn't hurt too much