How can I determine whether my processor is 32-bit or 64-bit?

Another way would be to use CPU-Z. In addition to bitness (AMD64 or EM64T) of the processor, it will display other useful characteristics of the processor.

Another way would be to check directly on the website of the manufacturer. Intel has a database of its processors here and it's quite nice. Unfortunately, AMD does not have such nice interface, but you can always go to their homepage and poke around. Here is the list of their desktop processors. VIA's processors seem to be listed here.

You could search google/newegg for your particular processor, if you know it by name, and read the specs. The specs on your processor says: 64-Bit Support: Yes. http://www.newegg.com/Product/Product.aspx?Item=N82E16819103254

But i'd vote for someone else's answer if they could give a quick and easy way to check this without having to know your processor's model. Maybe it says in the bios on boot up?

What OS are you on?

In Linux / Mac OS X all you have to do is open a terminal and type uname -p