We recently discussed the benefits of responsive websites. Responsive websites are great if you want your site to be functional no matter what device it is viewed on. Responsive sites certainly improve the usability of your website, but do not affect your search results.
Although many believe that responsive designs give you a rankings boost on Google and Bing, Google has finally set the record straight. John Mueller of Google officially confirmed this in a recent Google Webmasters Hangout.
The reason that some are under the impression that responsive designs will help your rankings is that Google did announce it will demote non mobile-friendly websites last year.
Despite not giving your website a ranking boost, responsive designs are still something that web designers should strive to use. By making the site more user-friendly, you are increasing the chance of visitors staying on the site, and ideally, performing an action (i.e. filling out a contact form, subscribing to a newsletter, clicking an e-mail address or phone number).
If a website ranks well in search results, but is not user-friendly and generally difficult to navigate, it is unlikely that users will spend much time on your site.