Guy Thomas, whose Ezine I've linked to a few times before, does a pretty good job explaining that "Yes, you can run 32-bit apps on 64-bit OSs". He continues by going into the detail of why.

What I find is that many admins get confused with the 64-bit driver problem. They see that drivers are required to be at the 64-bit level, and that requirement gets (incorrectly) transferred into the realm of applications as well. But Microsoft's 64-bit OSs have a "Windows on Windows" system that enables the necessary emulation required to run 32-bit apps. This is more or less the same WoW system that we originally saw way back in Windows 95 that allowed 16-bit apps to run atop its 32-bit environment.

Guy writes:

When in comes to interacting with a 64-bit operating system, programs and drivers are like chalk and cheese. Although I keep saying most 32-bit programs do work on 64-bit operating systems, many software companies will tell you, 'Our utility is not supported on 64-bit systems', and give the impression that it won't work. Whereas most hardware companies pretend their is no problem with a 32-bit driver for a 64-bit operating system, or they say a new driver will released next week, oh sorry next month, Ok maybe next year. Incidentally, 32-bit programs or drivers are often referred to as x86.

Drivers are like jockeys, they ride the hardware devices. Just as flat jockeys dislike jumping over hurdles or fences, so 32-bit drivers complain about driving 64-bit hardware. Printers, graphic cards, and sound cards all need special 64-bit drivers. When I installed a 64-bit version of Vista I was able to keep my old printer and my old monitor, but I did have trouble configuring the correct 64-bit drivers.

Software programs are shielded from the 64-bit architecture by the operating system; consequently, thanks to WoW64, there is a good chance of compatibility. Guy bets your old 32-bit program will work on 64-bit Vista. However, I did lose a foolish bet that Edlin would run on my 64-bit Windows Server 2008. As Edlin is a 16-bit program that it failed should have been surprise. As I write this, my old fiend 'Barking' Eddie is working on a compiler to get this 1980's command-line editor working on 64-bit systems. Why is Eddie doing this? - Nobody knows!

One thing that Guy doesn't mention is that the backwards compatibility only goes back one step. Thus, 64-bit Vista and Server 2008 don't have a built-in emulation system for 16-bit applications. Thus, if you yet maintain these oldies-but-goodies, you'll need to either remain with the 32-bit edition for now or host them via Terminal Services.

There's more on Guy's blog at: http://computerperformance.co.uk/ezine/BestPractice/BestPractice148.htm