There's no hardware as such that you need to run a 64Bit OS. It's generally recommended that you have a reasonably fast system with 4GB or more RAM as 64 Bit applications are able to make use of it. More importantly, not too many 64Bit specific applications are available right now. However, that will increase in the near future as more and more people adopt a 64Bit platform.
Are you looking to build a new PC to run the new OS?
pretty much. not that all hardware will run fast with it though. like ritwik said, just make sure you have 4g of ram and you should be all set. I know my laptop is capable of 64 bit operation, but it only has 3G of ram, so i went with 32 bit.
I have 64bit win 7 OS running 3GB of ram dual C.
How are you running 3GB in dual channel? I don't think it's possible to run dual channel without even number of memory modules.
Anyhow, if you say that your performance has increased, stick to the 64Bit OS.
From a historical standpoint, this is completely untrue. Chipsets as "recent" as the Intel 915 were 32 bit hardware. As a consequence of this, even certain Pentium 4 CPUs (Cedar Mill) were not compatible with these boards.