In the not so distant past, you could afford to get away with a website that wasn’t responsive. After all, that’s still somewhat of a new development. To briefly sum it up, responsive websites are those that adjust content on a web page based on the size/shape of the screen you’re viewing it on.
Today, you shouldn’t (and I personally would say you can’t) avoid making your website responsive any longer. The mobile market is huge – it accounts for almost 50% of all web traffic. Proof of its importance? Google announced in late April that mobile-friendly design will affect how search results rank, with mobile-friendly pages being favoured: http://googlewebmastercentral.blogspot.ca/2015/04/rolling-out-mobile-friendly-update.html
Responsive web design is not just the way of the future. It’s the way right now. So if you’re not on the right path as of this moment, get on it.