Well I have 12gb of ram, and I've never seen Crysis or wars use more than 2gb of ram in Win 7 x64. In total memory usage I never go over 4gb. I have been crashing way too frequently just recently, but I do not think it's Ram causing me to crash. Since I lowered AA to 0xAA, I am using less VRam, so it isn't getting maxed so often, I don't crash.
So I have a feeling crashing (At least for me) has something to do with my VRam maxing out on my Graphic card. Now since I have 5970 with 2gb (1gb of ram per GPU) I'm a bit gutted >.<
Since I'm running this game on max settings, 1900x1200, with or without AA, DX10, x64 and I can't get my total memory usage to hit over 4gb, I don't think most people are going to struggle to run this game with just 4gb of ram. That said, having a bit more, never hurts.
*Edit* After joining the snowy map, can't remember the name of it, my memory did spike to 5gb, and then drop to 4.1gb. But I blame all that snow constantly on the screen....