Minimum requirements for NVIDIA's Ambient Occlusion:

+ Windows Vista or later.
+ Recent NVIDIA driver, oldest possible version 301.24.

Further requirements and limitations:

+ NVIDIA's 3D Stereo features must be turned off - the driver can not handle both, 3D Stereo and AO, at once.
+ AO can only be used for AW's D3D Renderer.
+ UAC must be lowered for User Mode Applications accessing the NVIDIA's driver API of AO.

After all requirements are met, please check aworld.log for detailed messages appearing the section labeled NVAPI.

According to NVIDIA's documentation, all cards after GeForce 8500 are supposed to support AO. OEM cards may differ in their specifications.

For troubleshooting, please check out ActiveWiki.
For in-depth technical analyses of NVIDIA cards, we recommend NVIDIA Inspector.