Seen so many unanswered post on this problem that I though I'd offer a temp workaround.
The problem seems to occur when updating Crysis 2 to v1.9. When you try to resume an exisiting game the program locks and you get a recurring message "Crysis 2 has stopped working" "shut down game or check online"

I have an E8400 3Ghz, a HD5850 and 23" 120Hz 3d screen. My system is no slouch but the problem definately seems to be linked with patch v1.9 and a combo of certain hardware.

This is only a temp fix until the developers get their finger out and issue a v2.0 patch.
Google - Crysis 2 1.8 patch download
Download the 1.8 patch to desktop
Reinstall Crysis 2 (your profile is retained)
Refuse to download 1.9 patch
Install 1.8 patch
Game will now RESUME

The downside to using this method is all fix's from 1.9 are not installed, neither is directx 11 and new textures. The game certainly doesn't look as good as it does with the latest updates but at least it is playable.
Personally I'm going to putsh Crysis 2 to aside until a new update shows up as I prefer playing with the eye candy.

And the downside is that you can't play the multiplayer

True. Should have made that clear but was aiming at those who still can't get thru the single player mode.