Matt Cutts validates the relevance of backlinks in his latest video yet again. Backlink Relevancy Is a Big Win In Terms Of Search Quality, so Google sticks to it.
The question about a version of search engine that excludes backlink relevancy was answered by Google’s head of search spam, in this video.
In reply to this, Matt Cutts says that there is no version of Google available to the public which has no backlinks relevancy. He also clarifies that the Google team has experimented without backlinks relevance but it turned out worse for search quality.
The video concludes that even though there is lot of spam but the relevance of backlinks is a plus for keeping the search quality high. So, the Incoming, inbound or inward links, whatsoever you call them, they are important to boost your search engine rankings.