Maybe the paper that started it all, Brin and Page's "The Anatomy of a Large-Scale Hypertextual Web Search Engine" (http://infolab.stanford.edu/~backrub/google.html), has still something to tell us. Among the other ideas expressed in the paper, I find this interesting (in "6.1. Future Work"):

"Simple experiments indicate PageRank can be personalized by increasing the weight of a user's home page or bookmarks."

This would be great. I know that Google has done something in the direction of personalization, with Personalized Search (2004) and Custom Search Engine (2006), but I think that the idea Brin and Page proposed in 1998 is something different, because not every search you do or every search-result-link you click is the same for you (PS), and knowing that a site is good does'nt mean only that you want "to restrict your search results to include only these pages and sites, or simply to give these pages and sites higher priority and ranking" (CSE). It would be great if you, finding a good site, could give its outlinks more weight in your future searches (ever better if you could do the same with the sites that links to it).

Maybe they dont'have now the power to calculate a pagerank for every webpage not once but million times (one for every user)?

(Are there, in your opinion, other ideas in the 1998 paper never used but still interesting?)

The idea of a user input about the authority of some documents (in a network of documents) is develped here (in a far too technical way for me...): http://www.cs.umass.edu/~mccallum/papers/lift-icml2000.ps

Three methods to personalize PageRank are analyzed here: http://www-cs-students.stanford.edu/~taherh/papers/comparison.pdf (technical...)