For certain games, patching will resolve the problem running under Windows 7 64-bit. Patches can usually be downloaded from the support website of the game in question, although if you’re running games in Steam it will be automatically applied to your installation.
In the future, problems between 32-bit games and 64-bit operating systems and hardware will become a thing of the past as more and more users adopt 64-bit architectures (namely motherboards and CPU's). As with the death of 16-bit computing, this is something that will happen naturally over the next 5 to 10 years.
Additionally there are third party patches available that fudge around with the available memory on your system to force compatibility with any problem games an applications.
However, if you’re a gamer who has concerns over Windows 7 64-bit game compatibility, your best option is to stick with Windows 7 32-bit at least until a patch for your intended game is available, and certainly until all issues that might affect you are resolved.
(Images via www.amazon.co.uk)