For a small number of implementations, the PHP timeout and hosting conditions are such that the Upgrade Process runs out of time before the Installer has had time to finish. In those cases, the upgrade fails and the site is not properly updated and files are missing. In some cases, nearly all files might be missing. Depending on how far the Upgrade process got, the errors you might experience could vary. Generally speaking, you will see some kind of message about missing files.
Although this is a very concerning problem to have, it can be easily fixed. Simply take a full install package for the release, unzip it, and copy ALL of the files to your website, replacing the files already there. Doing so will fix the install and your website should work fine.
For the future: a work-around fix was applied to Joomla 1.6.4 to help resolve this problem by resetting the PHP time used to 0 during the unzip process and during the file copy process. This will help prevent time out situations and therefore avoid failed updates for the 1.7 upgrade (or 1.6.5, if that release comes first).