Not everything, but quite a lot. It is only one factor in the algo but a pretty important one all the same.
I worked on a site a couple of years ago in a fairly competitive industry. Once the work was done and links from other authority sites came in (mainly informational sites) the site went to the top of just about every important and relevant keyphrase. I no longer touch the site and haven't for over a year. I see this site as now being one of the authority sites in the industry. This is important as it helps keep it above other newer sites aiming for the top.
On my latest sites I am attempting to apply the same principles of providing the best information and collecting the best inbound links. This should - over time, and the time frame is getting longer - lead to stable high rankings and authority status.
Just my £0.02 :)