All you need in order to know how important and relevant responsive design has become is to look at the percentage of people who are using mobile devices in order to browse and navigate the internet. There are some areas in the world that have more than 50% of the internet users login in with their smartphones and not with laptops or desktop computers.
The good news is that creating your website with a responsive design is a lot easier than you think. All you need to do is start using WordPress and most of the templates available are responsive, so you will have no problem creating a proper responsive site.