When considering a Magento upgrade one of the most important things you should discuss with the person who might do the upgrade is whether the changes you think the upgrade will make are actually going to happen. We often have people come to us for upgrades of Magento or other web software who are expecting that it will fix a problem they are having, but in most cases the upgrade won’t have any impact (in many cases fixing the problem requires much less work that an upgrade would entail). Along similar lines we have had an increasing number of people coming to us asking about Magento upgrades who it turns out are actually interested in making their website responsive; that is making the website work well across desktops, tablets, and smartphones.
Upgrading Magento will not make a website responsive. The confusion surrounding this seems like it might be largely due to how Magento 1.9 was promoted by its developers. The blog post announcing that version is titled “Magento Enables Responsive Sites in Half the Time” and the clearest mention of what that actually means in the post isn’t all that clear. It states that a “new responsive design reference theme that makes it possible to quickly get a tablet and smart phone-friendly site”, what isn’t necessarily clear for someone who doesn’t deal with the more technical side of Magento is that all that means that Magento now comes with a new theme that is responsive. The new theme doesn’t have any impact on the existing theme you have, so you would have to switch to new theme to make the website responsive. With that you lose the current look of the website and would have to customize the default theme.
Since responsiveness comes from the theme and not from using a newer version of Magento, if you are looking to make your Magento website responsive you would want to replace your current theme with one that is responsive. You could customize the new default responsive theme that comes with Magento 1.9 & up, or you could use another responsive theme created by someone else as well. Depending on if the new theme is compatible with your Magento version you may or may not need to upgrade Magento as well.