Improved Search Engine Rankings

Google has long recommended utilizing responsive website design to help various devices and screen sizes, however, the web index made this suggestion a stride further a year ago when they started including a "Mobile-Friendly" mark to sites that utilized this methodology when those destinations showed up in a search results page on a mobile phone.

While this assignment was pleasant to have, Google said at the time that they imagined utilizing mobile-friendliness as a positioning sign later on. 

Perhaps the greatest preferred position of having a responsive website design is improved web crawler rankings. 
Google thinks about all site responsiveness as one of the determiners of their position in the web crawler results. This possibly implies when your site isn't responsive, it will naturally be put lower in the web index results