Not long ago, it was easy to design a website. It would often only need to come in small set of sizes as screens didn't vary much but technology has burst forward with all sorts of devices and laptop screen sizes - not to mention the variety of desktop monitor sizes. The biggest challenge was getting a website to work across different browsers.
Responsive web design (RWD)
Thankfully browsers are converging in their capabilities but the new challenge in the world of website design is the sheer number of different devices that people use to browse the internet. The principle of RWD is that website can respond flexibly to any browser size including unknown future devices. This means RWD is inherently future friendly.
If you nail mobile, then you will probably nail desktop. When someone browses on a small screen such as their phone, they need to be engaged as people often will then visit the site on their laptop or other larger screen device. Serve them up rubbish on their phone and they may forget your site and go elsewhere.
When I create new websites I they come responsive as standard.