If I had a kitten for every time we've been asked “Does my site need to be responsive?” I would be that crazy cat lady that lives down the street.
But, seriously, Aaron captured our thoughts on it perfectly in a recent interview in .net:
I think all sites should be capable of adapting to whatever device is being used to access them. To me it’s about offering good customer service and not forcibly ejecting someone from your website (or making them endure a crappy experience) because they happen to be using a browser you don’t like or didn’t bother testing. That’s why we at Easy Designs follow the philosophy of progressive enhancement. And mobile-first, responsive web design is a great tool in the progressive enhancement tool chest.