Minimum Requirements
CPU: Athlon 64 3000+/Intel 2.8ghz
Graphics: Nvidia 6600/X800GTO (SM 2.0)
RAM: 768Mb/1Gb on Windows Vista
HDD: 6GB
Internet: 256k+
Optical Drive: DVD
Software: DX9.0c with Windows XP
Recommended Requirements
CPU: Dual-core CPU (Athlon X2/Pentium D)
Graphics: Nvidia 7800GTX/ATI X1800XT (SM 3.0) or DX10 equivalent
RAM: 1.5Gb
HDD: 6GB
Internet: 512k+ (128k+ upstream)
Optical Drive: DVD
Software: DX10 with Windows Vista
Crysis is a very demanding game if you want it to run at top-notch. However, the minimum requirements aren't too bad, mostly because CryENGINE 2 can be pretty flexible.
I'm so glad Crytek is giving the user some flexibility. If you don't have DirectX 10, don't worry. Crysis will still play with good visuals even with DirectX 9.0, but it won't be at it's best. If you get a DirectX 10 video card and have Windows Vista, you can just go to the in-game menu and at the click of the mouse, switch from DirectX 9.0 mode to DirectX 10 and enjoy improved graphics. It's that easy.
Of course, Crytek's poor choice of using EA as the publisher...can't say much about that. Ubisoft is far better.