AMD has a 3D option with passive glasses, but you are limited to a very few supported monitors (like 2 or 3), and you need to get the hardware from various non-AMD vendors. I have not read any reviews of this new implementation of passive 3D.
I have tried 3D Vision on an Nvidia setup, and it was mind-blowing. If you are serious, it would be easier to go with a single GTX 570 with the 3D Vision kit, which includes active shutter glasses that are synced to the monitor. You would still need to research whether your current TV is compatible. Having an AMD motherboard will not limit you to AMD video cards.