Fatal error: Class 'Mage_Install_Controller_Router_Install' not found in /var/www/.../public_html/app/code/core/Mage/Core/Controller/Varien/Front.php on line 138
We did not get this error after SUPEE 5994 as others did.
It is not due to compilation (that has been disabled and cleared), cache (both main cache and sessions have been emptied several times, PHP opcache is disabled), nor the server itself (have restarted Apache and the entire box). The file definitely exists (others report patching failed to create it) and has the right owner and permissions.
I'm guessing that the file isn't able to be autoloaded but I don't know why.
I tried commenting out the router conf (as per this answer) and manually clearing the cache again. This does prevent the fatal error, as Magento no longer tries to load the file, but that isn't a solution because that code needs to be there to patch a hole.