From MS website:
Most programs designed for a computer running a 32-bit version of Windows will work on a computer running 64-bit versions of Windows. Notable exceptions are many antivirus programs, and some hardware drivers.
Drivers designed for 32-bit versions of Windows don't work on computers running a 64-bit version of Windows. 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. For information about updating drivers and troubleshooting issues with device drivers for 64-bit versions of Windows, contact the manufacturer of the device or program.
I highlighted the AV piece - you will certainly have to have a 64-bit version of your AV software as well as 64-bit drivers for peripherals.
Also, it is worth pointing out that 16-bit apps will most certainly NOT work in a 64-bit environment - the Windows-on-Windows (WOW 64) abstraction layer only works "one step" back - i.e. 32-bit on 64, 16-bit on 32.
Finally, while most 32-bit apps will run in a 64-bit environment, they will not be able to take advantage of the 64-bit OS, so will not run as efficiently as a native 64-bit app. This really is unlikely to be a problem for a single-user PC (that spends 99.99% of CPU cycles waiting for user input!), but can be a problem on servers.
SD