If for some reason you need to enable Basic Authentication, you can do so quickly through the Exchange Management Shell. This is sometimes needed if you're migrating to Exchange from another (third-party) e-mail provider.
If you do not know what Basic Authentication is, you do not need this!
Start up EMS as an account which has the required permissions to make changes to the virtual directories used by Exchange. Then, run this:
Set-WebServicesVirtualDirectory -Identity "EWS (Default Web Site)" -BasicAuthentication $true
Note that Office365 has Basic Authentication enabled by default.