Why does iTunes not recognise a plugged in iPhone on Windows 8.1?
This technique just worked for me on 11.1.3.8 (it broke on the Windows 8 to 8.1 upgrade):


Control Panel, uninstall "iTunes" and "Apple Mobile Device Support"
Plug out your iDevice(s)
Reboot (might be unnecessary, but Windows 2.0 trained me to do this all the time after driver changes)
Run the iTunes installer (you might already have downloaded it)
Plug in your iDevice(s)


At this point, my iPod and iPad were recognized and synced.  My library appears to be intact as well.

I subsequently rebooted and these devices are still found.