All search engines use link popularity as part of their algorithm. Because Google was the search engine that initially created a ranking system based on hyperlinks, I will use it as an example. As Sergey Brin and Larry Page were developing the Google algorithm, they created a ranking system, called PageRank™. PageRank, also known as PR in the webmaster community, gives each page a certain value based on the links pointing to it. Google considers a link from page A to page B to be a vote, by page A to page B. In essence, the more votes a particular page gets, the more important that page is considered by Google. In addition, Google also takes into consideration the value of the page where the link is placed; the more important that page is, the more value the vote has. (Google d.)
Google does not reveal the actual scale that it uses for PageRank calculations, but the Google Toolbar uses a scale of 1 to 10, with 10 being the highest. The PageRank scale is logarithmic, which means that the step from 9 to 10 is much bigger than the step from 1 to 2. The PageRank of each page can be seen with the Google Toolbar, located at http://toolbar.google.com/.