The answer is yes. Windows 7 64-bit supports almost all 32-bit applications. 64-bit systems emulate 32-bit applications, so all 32-bit applications can run smoothly on 64-bit systems. There are exceptions (read on).
If you look in your system folder, you will find a folder called “WoW64” (Windows-on-Windows 64-bit), which is basically a subsystem on your system that is capable of running 32-bit code.
Are there any 32-bit programs that won’t work on 64-bit Windows 7?
Yes. There are some exceptions. Many anti-virus and firewall solutions designed for a 32-bit system will not run on a 64-bit Windows 7 and require a special 64-bit installer. Most software providers also allow you to download a 64-bit version of their applications.
Also, any device drivers designed for 32-bit systems won’t work on 64-bit systems. So, don’t try to use your old drivers on Windows 7 x64, it won’t work.
So, yes, Windows 7 64 can run 32 bit programs!
Update: More exceptions include Photoshop and basically all Adobe products. Adobe released a special 64-bit edition for 64-bit systems.