Most programs designed for the 32-bit version of Windows will work on the 64-bit version of Windows, with the exception of many antivirus programs. However, keep in mind that device drivers designed for 32-bit will not work on 64-bit computers. Therefore, if you're trying to install a printer or other device that ONLY has 32-bit drivers available, it won't work correctly on a 64-bit version of Windows.
Hope this makes sense!
Microsoft Windows Outreach