After installing patch 8788 i received mails from customers that the user registration/login is not working anymore in the checkout. The user login outside the checkout page is still working.
System > Configuration > (Change to Store View) > Developer
Open the Developer area and add your IP to the whitelist, then enable the profiler and reload your login page. You should see dotted lines encompassing areas of the website, each with their own directory path for the file being used to load that area.
Check the registration/login page directory path to make sure you are updating the correct .phtml files. You may have an extension that is overriding your registration/login pages but doesn't look any different than the default.
This and pong's answer should solve your issue. Remember to flush cache and reindex after changes like this.