I had been using Windows 8 and TortoiseSVN icons have been displaying properly, but after installing Windows 10 I can no longer see the icons for the files/folder status.
As in current recommended answer mentioned, you need to sort the entries of the overlay identifiers in the registry. I haven't deleted those OneDrive or GoogleDrive entries but renamed all Tortoise Folders by adding 3 spaces to bring them on top. Just restart and even with Tortoise SVN client 1.7.9 you'll see your SVN overlay icons under Windows 10 again.
I was using Subversion 1.7.x and installing the version 1.9.1 or modifying the registry entries did not solve this issue of icon overlays.
In my case, after using SVN upgrade working copy the icon overlays for the upgraded project appeared.
In conclusion, old projects using Subversion 1.7.x do not show icons and projects using Subversion 1.9.x do (under Windows 10).
Tip: there is a button that takes you to the registry in Settings -> Icon Overlays -> Overlay Handlers -> Start registry editor. At least in version 1.9.1