There are changes on the horizon. As we step into the world of voice search, where users don't always have convenient links to click on, I wouldn't be surprised to see linkless mentions become more important to SEO than ever before.
Links are, no doubt, still vital to organic rankings. Study after study finds that there is a strong correlation between link signals and SERP results, as does the industry survey we at Link-Assistant conducted. And Google has firmly stated that PageRank is still a key ranking signal.
Most important, links matter because of what they represent: user trust. As search engines get better at understanding user sentiment (i.e., interpreting what content users value, which sources they trust, and whose opinions they listen to), there's a very real possibility that linkless mentions could one day be weighed as heavily as actual links.
In fact, we already know that sentiment analysis plays a big role in some search engine ranking algorithms.
Bing has always been a little more forthright than Google about how its ranking algorithm works, which is why we know that sentiment analysis and social signals are part of its strategy. Understanding sentiment is key to understanding what to trust, according to Bing.
The evidence for that comes mainly from Bing's Webmaster Guidelines, which state: "Social media plays a role in today's effort to rank well in search results. The most obvious part it plays is via influence. If you are influential socially, this leads to your followers sharing your information widely, which in turn results in Bing seeing these positive signals. These positive signals can have an impact on how you rank organically in the long run."
Furthermore, at an SMX West event, a former Bing sr. product manager stated: "Years ago, Bing figured out context and sentiment of tone, and how to associate mentions without a link. As the volume grows and trustworthiness of this mention is known, you'll get a bump in rankings as a trial."