Apparently more than 50% of web searches now originate on mobile devices and Google recently announced that mobile-friendliness will be a ranking signal from April 21st 2015.
A Google Engineer suggests this change will affect as many websites as the Panda and Penguin algorithm updates and industry experts have christened this latest algorithm update, "mobilegeddon".
Responsive Templates
The best way to ensure your Joomla website search ranking is preserved is to implement a responsive template if you don't already have one.
Responsive templates are available for Joomla 2.5 and there were even a few for Joomla 1.5 but Joomla 1.5 and Joomla 2.5 are already "end-of-life" and you should ideally migrate to Joomla 3.x which ships with Bootstrap and already includes some responsive templates.
robots.txt Changes
If you installed Joomla prior to version 3.3, you will likely need to amend your robots.txt file to ensure that Google can access CSS, JavaScript and other files in your template folder to confirm your website is mobile friendly.
Mobile Friendly Testing and Official Instructions from Google
Google has provided a test tool at http://www.google.com/webmasters/tools/mobile-friendly/ so you can check that your website is ticking all the relevant check boxes.
Google has also provided instructions on how best to make your website mobile friendly including specific instructions for Joomla, WordPress and other popular platforms.
More Information
For more information see:
http://searchenginewatch.com/sew/how-to/2398591/-mobilegeddon-is-coming-on-april-21-are-you-ready
http://www.entrepreneur.com/article/244175
http://www.didit.com/mobilegeddon-tip-of-the-week-examine-your-robots-txt-file/
http://www.stemlegal.com/strategyblog/2015/mobilegeddon-the-countdown-is-on/