Due to Major changes in Media Editing and MySQLi for PHP v5.5, some sites might face severe issues.
I strongly suggest to have a backup for both wordpress files and DB before updating to WP v3.9
After having backups, members must follow instructions by @joesell89.
If anyone face errors or bugs, then either deactivating all plugins or renaming each plugin's folder will allow access to sites backend. Then activate or rename plugin folder one by one then find out who is the culprit for your site. Then report the bug for the same to the concern plugin support forum to resolve the issues from plugin authors.
If the above method doesn'nt work then delete previously installed wp files. Now revert to your previous state by uploading both backups wp files and DB taken earlier. Now your site back to the previous state.
For major changes in WP latest version v3.9, give a read for the following:
WP v3.9 major changes
WordPress 3.9 Smith