Websites running the first versions of Joomla! are becoming increasingly targeted by hackers. I dont build websites on Joomla! personally prefering to build most of my sites on the more robust WordPress platform. If you are running an old version of Joomla! I would suggest that you either upgrade as soon as possible to avoid your website being compromised or look towards a redesign on a different Content Management System. All versions of Joomla! 1 are no longer being patched by developers as it is end of life.
If you are running a Joomla! v1.x site I would urge you to upgrade to either version 2.5 (recommended for production use) or version 3.0 (recommended for developers and early adopters).
To find out which Joomla! version you’re currently running, check the footer of your administration panel or look in libraries/joomla/version.php.
For general advice about upgrading, please refer to this Upgrading and Migrating Joomla! documentation.
Other Security Considerations
Please remember that upgrading to the latest version of Joomla! isn’t a cure-all solution, and any third party add-ons or templates can have potential security flaws. Be vigilant when installing any extras, delete old files you aren’t using any more, and try to download from official trusted sources.
Please note: I cannot upgrade versions of Joomla! websites but I do know some developers that can do this.