With tomorrow’s Anniversary Update for Windows 10, Cortana becomes the Windows-Internal search engine with Online access, regardless if you want it or not.

Cortana, get lost!

Getting rid of Cortana

You can still disable Cortana by fiddling around in the registry

Machine global:
HKEY_LOCAL_MACHINE\SOFTWARE\Policies\Microsoft\Windows\Windows Search
Only for current user:
HKEY_CURRENT_USER\SOFTWARE\Policies\Microsoft\Windows\Windows Search

In both cases, set the value to "" (DWORD type)

I’ve not yet tried it, since I’m still waiting for the Update. In case you don’t want to mess up with the registry, you can download the Regkey-Files from the article page.