In a Google+ webmaster hangout from a couple weeks ago, Google's John Mueller was at the GooglePlex and had a hangout with two of his colleagues.
Josh asked at 26 minutes and 3 seconds in, why does Google use links for ranking at the level they do. He said, Google should use other means to rank sites. Of course, he knows they do use other factors but his point was why do they place so much weight on links.
John Mueller answered that saying they do have tons of other factors outside of just links.
John then said he has a friend of his who is “back home” in Zurich, his friend just put up a new web site for the local neighborhood. The new site does not have any links at all and over 300 pages are indexed and pages are ranking and they are getting a lot of traffic from search.
No one ever linked to the site ever, he said, but they did submit sitemaps to Google and they have an RSS feed.
The web site does fairly well without any links at all, John said. So it is not the case you absolutely need links to rank, he added. John did say that links are "obviously" it is part of Google’s ranking factors, but it isn’t something Google only relies on.
We know a year ago, Matt Cutts said Google did try turning off links in their ranking algorithm and the results were horrible. We also know that Yandex, the huge Russian search engine, did remove links from a niche segment in their ranking algorithm when that segment was spammed to death.
Here is the video embed at the start time:
Forum discussion at Google+.