Is having a responsive site important?
My answer to this question is, absolutely. Now, that being said, if your website already has a separate Mobile website, then you should be alright or at least better off than all those who just have an old school website (non-responsive). However, to have a website and a mobile site often means you have paid for two sites (increased cost) and often means that you have to update content in two places or sometimes have to manage two sets of images and content. It is possible to have a mobile site pull content and images from a normal non-responsive website, but it still means two code bases and special code to detect and redirect users based on the device type they are coming from… Long story short, a website and then a separate mobile site still means more to test, additional complexities in content loading, and more code to manage and host. So, my opinion is that responsive design/responsive website is the way to go, but don’t just take my word for it, here is a great article from Search Engine Land about how not having a mobile friendly presence can actually ding you in search.
How Much Traffic Will You Lose From The Upcoming Mobile SEO-Pocalypse?