32 bit applications (say, MS Office 2003) run just fine under 64-bit Windows 7. Some need to run in a compatibility mode (the same as with Vista, as Win7 is built upon Vista's foundation).
I installed the 64-bit (enterprise edition) of Win7 under Parallels 4, and recently upgraded to Parallels 5. The 64-bit Win7 VM works just fine there as well.
The Windows world has the same confusion as the Mac world regarding 64-bitness. The biggest difference lies with device drivers. 64-bit Win7 REQUIRES 64-bit drivers for hardware. It transparently runs both 32-bit and 64-bit applications without problems, as long as they do not depend on specific hardware (e.g., printers or audio cards) drivers.
