With Vista and up, 64-bit versions of Windows no longer support 16-bit programs, but 32-bit versions can still run them. Windows 8 has changed a lot of things from even Windows 7, and there were rumors a while back that it would only be available in 64-bit which seems not to be the case anymore. It’s no secret thet Microsoft is pushing users to migrate to 64-bit systems. Have they dropped 16-bit support from Windows 8 altogether (including 32-bit versions)?
This is the same as Windows Vista or Windows 7. If you have a 64bit version of Windows, you cannot run 16bit applications. If you have a 32bit version of Windows, you can run 16bit applications.
Workaround for 64bit systems: In Windows 7 64bit you could just download the Virtual PC XP Mode and run your 16bit application there. I'm not sure if Windows 8 also provides an XP Mode (I don't think so) but (some versions?) of Windows 8 come with Hyper-V support. So you could easily run e.g. Windows XP in your Hyper-v to have 16bit support.
As per Windows 7, 16-bit applications simply cannot run on a 64-bit Windows 8 installation.
However, the NTVDM required to run 16-bit applications is still available on 32-bit Windows 8 systems:
The NTVDM is present in all 32-bit NT-based Windows versions including Vista, 7 and 8, except for in 64-bit versions.
As Synetech noted, this feature is disable by default and must be manually enabled.