Does having a mobile friendly website effect search results?

In short, yes! Google just announced that they are factoring whether or not a website is responsive into their algorithm.

An explanation by Google released on their blog explained it like this. Many sites have mobile versions of their content, but the problem is many sites only have one page optimized for mobile. What happens are these sites with only one mobile optimized page, they would redirect any page to the mobile Optimize page. So when you as a user searched for Red shoes, you might find a sub page of the site that was relevant to red shoes. When you click on that link in the search results, the site you were clicking to would automatically redirect you to a mobile friendly page that had nothing to do with red shoes. That would cause a bad results in bad experience for the user.

So if your site is not mobile responsive, your desktop search results will be different than tablet or smart phone search results. With smart phone and tablet search growing more and more popular, it’s very important that your site is not only mobile optimized but also mobile responsive so that users on tablets and smartphones will have a great experience and research rankings will also be improved.

There is no definitive word on how having a responsive site will play into desktop search results.