It's come out that Microsoft has had Windows download Windows 10's installation files (at least 3GB).  For those who wish to stay with their existing version and may want to save unnecessary bandwidth use (and possible expense), there is a way to prevent Windows from making that assumption.

Firstly, you'll need to download and install a patch from Microsoft.  If you're running Windows 7, download it here; for Windows 8, here.

Secondly, you'll need to change one setting in the Windows Registry.  Open up your registry editor using the Start Menu search or by pressing WIN + R and typing regedit and hitting enter, and then navigate down to the following key:

HKEY_LOCAL_MACHINESOFTWAREPoliciesMicrosoftWindowsWindowsUpdate

The WindowsUpdate key so you may have to create it by right-clicking the Windows node.  Once the WindowsUpdate key is present, right-click that and create a new 32-bit DWORD can name it "DisableOSUpgrade".  Lastly, give it a value of 1.

If you find that possibly a bit overwhelming, and some might, you can download a registry file that, once copied to your system, you can right-click and Merge into your registry.  The zip file is available from the good folks at HowToGeek.com

Once done, reboot.