Is there even a reason why I should be asking this question? I'm sure it would run but just in case I want to know if it's perfectly safe for me to assume that all hardware drivers will be supported? I have a good laptop that's running Windows 7 RC 7100 32-bit and have my MAPS Win7 Pro 64-bit DVD handy with me... and fidgeting...!
The Windows 7 Upgrade Advisor will tell you with certainty whether your computer meets the requirements for Windows 7 x86 or x64.
The quickest way is to post the CPU information and we can tell you!
Press Windows Flag+Pause/Break then look where it says Processor.
Google that information or look on either Intel or on AMD for the CPU and see if it is compatible. That being said, nearly every mainstream (and some budget) CPUs in the last couple of years have been 64 bit.
There is a free utility called Securable that reports the maximum bit length, as well as some other features of the processor it is run on. If this reports 64 bits, you should be good to go.