How can I prevent Windows 8.1 upgrading to Windows 10?

With the later updates to Windows 7 and 8.1 relating to the "Get Windows 10" (GwX) notification system there was also support for disabling the notifications.

Microsoft KB3080351 describes the somewhat finicky steps to do this (involves registry changes or Group Policy Editor).

Subkey: HKLM\SOFTWARE\Policies\Microsoft\Windows\WindowsUpdate
DWORD value: DisableOSUpgrade = 1

Subkey: HKLM\Software\Policies\Microsoft\Windows\Gwx
DWORD value: DisableGwx = 1

There is also a third-party tool Never10 which automates the process described in the above KB article.