Is it possible to launch 64-bit applications in a 32-bit operating system?

While developing 64-bit applications (especially crossplatform ones), developers often wish to provide compatibility with 32-bit operating systems which still occupy a significant part on market of operating systems. Unfortunately, direct execution of such applications is possible only on some 32-bit operating systems. Thus, for instance, Mac OS X supports both the 32-bit and 64-bit modes. The kernel operating mode is chosen when launching the system.
For operating systems of the Linux family, there is the project LinuxPAE64 that allows to execute 64-bit applications in systems loaded with 32-bit core and device drivers but this project is far from being complete at the moment of writing this article.
In 32-bit operating systems of the Windows family, the only way to launch 64-bit applications is to use emulators and virtual machines, for instance, qemu and VMWare, but the necessity to emulate the 64-bit platform in this case greatly reduces the system's performance and the end user will have to purchase the 64-bit version of the operating system anyway.
So, it is reasonable to make two branches of the project intended to work in the 32-bit and 64-bit environments for the compatibility purpose. However, the task of maintaining 32-bit operating systems becomes less relevant and in time it will be quite natural if you have only the 64-bit version of a program.
If a developer cannot debug and maintain both 32-bit and 64-bit versions of a program and the software being created does not require too much memory and system performance, you may maintain only the 32-bit version since most of the existing 64-bit operating systems let you execute 32-bit software at the moment. But this step seems to be non-optimal in a long run since most operating system vendors focus on 64-bit platforms (for instance, MS Windows Server 2008 is the last server operating system by Microsoft that has a 32-bit version).
References

1. Discussion at Stackoverflow.com. "Is it possible to run the 64 bit application on a 32 bit OS?"