This is easily the most important aspect of SEO as far as I’m concerned. Even with Google moving further down the line of social indicators on which to base it’s results, these are still off-site aspects and should therefore receive the vast majority of your time/resources.
As mentioned earlier, a high ranking results from a combination of relevance and authority and these come almost entirely from other websites.
The ideal scenario would be if you were an authority website such as BBC or Wikipedia who naturally draw inbound links from a wide range of other websites due to their valuable content. If you produce content like this the draws thousands of links per day, you don’t have to worry about working on link-building, but for the rest of us, we have to aim to manipulate Google by simulating the behaviour of external websites linking to valuable content.
The ideal backlink is a text link from a page that is highly relevant to your target keyword phrase on a highly authoritative website that has content focussed mainly on that keyword with anchor text as closely matching the phrase you are trying to rank for as possible.
Unless you are producing amazing content, these types of links are extremely hard to come by so the best thing you can do is make up the authority and relevance separately by creating low-relevance, high authority links and also high-relevance, low authority links.