There are still some older applications, and some application installers that are 16 bit.

Some customers have only noticed it now that those applications don’t work when running on 64 bit Operating Systems.

The support of 16 bit on 64 bit platforms has never existed. SysWOW64 supports 32-bit, but not 16bit. Windows Server 2008 R2 will only available as x64 and Itanium (IA-64) editions. Windows 7 will be available as x86 and x64 editions.

Windows Version Supports 16 bit applications
Windows Server 2003 x86 Yes
Windows Server 2003 x64 No
Windows Server 2003 IA64 No
   
Windows XP x86 Yes
Windows XP x64 No
   
Windows Server 2003 R2 x86 Yes
Windows Server 2003 R2 x64 No
Windows Server 2003 R2 IA64 No
   
Windows Server 2008 x86 Yes
Windows Server 2008 x64 No
Windows Server 2008 IA64 No
   
Windows Vista x86 Yes
Windows Vista x64 No
   
Windows Server 2008 R2 x64 No
Windows Server 2008 R2 IA64 No
   
Windows 7 x86 Yes
Windows 7 x64 No

(x86 = 32 bit, x64 = 64 bit, IA64 = 64 bit)

If you are running a 16-bit application in this day and age, there must be a good reason. If the application is that important, then the investment should be made to redevelop it as long term solution. In the meantime, if you need to run it on a Server edition, you can run Windows Server 2008 x86 or Windows Server 2003 SP2 x86 in a Hyper-V Virtual Machine and run 16-bit applications on that Guest OS.