Responsive web design all boils down to user experience. If you can provide an optimal user experience to your website visitors, regardless of what device they are using to access it, you can set yourself apart from the old clunky websites that barely work on mobile devices (if at all).
Responsive design is a great way to "design once and deploy everywhere". What most people don't realize, is that it is just as easy (or easier) to build a responsive website than it is to build one the "old way". Most of my new clients don't even realize that I'm building their sites to be responsive until I present them for review. It's a nice little bonus for them.