If the goal of your website is to drive traffic through SEO then Backlinks are a must. My 14-year-old has a website where she stores her poetry. She does not need backlinks because she is not attempting to drive organic traffic.
That being said....the Quality of your backlinks matters a ton. Think of it this way...Google is essentially running a popularity contest. The sites/pages that have backlinks from Bigger more reputable sites in their niche usually win. I say "usually" because backlinks are only 1 of many ranking factors. In general, though, quality linking will contribute to the credibility and reputation of that website which is what Google - and potential customers - want.