Can i run 64-bit versions of windows?

Hi There.
Somehow i have told myself, that my system cant run 64-bit versions of windows.
I now want to upgrade to win7 or win8, and would like to buy the 64-bit version.
Now I cant seem to find evidence that i can´t run 64 bit, can u help me?

Intel Core 2 Quad Q9550 - 12 MB - 2.83GHz - BOX
MSI P45 - ATX - Socket 775 - Creative X-FI
ASUS ENGTX560 TI DC2 TOP/2DI/2GD5

Is there any other hardware, that can dertermine that?

Best regards
Flemming