Windows – install Windows 64-bit on a computer that has an Intel Core 2 Duo processor

The vast majority of new processors do.

If you have any doubts, and know the (potential) processor model, you can use the Intel website to find out.

This will lead you to a page like this:

Whereupon, if you click the specifications link, it will show you if 64 bit can be used:

There's not much reason nowadays to not use a 64bit OS if you have more than 3GB of memory, but if you don't you may wish to stick with 32bit just in case there are any compatibility problems - but at this point it will be rare if ever, especially with windows 7, and you may see a performance boost in some of your apps.

If this is for anything other than your home PC however, such as for something at your business, be sure to test any programs you rely on thoroughly first.