The page rank citation ranking system
It describes how Google works.
Google uses it for web documents, but it's useful for pretty much any directed graph structure. For non directed graph's it's subject to manipulation, but if you "trust" the nodes in the graph, then it will work for non directed graphs too.
One interesting application of it to programing would be to index libraries in source code as a ranking system in a code / api documentation search.
It would be really cool, for example, to build an index of something like source forge (or code plex), using "page rank" between types and methods as a relevance metric.
The easiest language to do it for would be Java (because Java namespaces use reverse domain names by convention).
I wrote a prototype of something like this when I worked at Microsoft. It indexed VB source code, api documentation, and compiled .net assemblies. It also did stemming of identifier names, recogonzing camel casing, pascal casing, and underscores, and split things up into multiple groups.
It got pretty good results.
I was pretty new though (I had only been there a couple weeks), I worked on a different team (the VB team), so I wasn't very successful in convincing the MSDN help folks to adopt it. They ended up just using Windows Live Search.
In any case....
Another use for it would be for Stack Overflow.
You could, for example, treat stack overflow as a large graph, with edges from people to documents, and from documents to people. If you then weighted the edges based on reputation, you could compute page rank over the graph, and then use the page rank to sort search results.
This would produce different results than what Google does (because the edges in normal page rank are not weighted), but I think for the purposes of searching Stack Overflow questions it would yield better results than Google.
I'm willing to bet that most links into stack overflow from the "outside" are to the main page, not to individual questions.
This means from Google's point of view, most stack overflow questions and answers are pretty much equivalent.
But, if you calculated page rank, using "reputation" to weight edges, you would get relevance results that reflected the values of the Stack Overflow community.
In any case... they paper is really good. You should read it.