Note: red links point to pages that haven't been written yet. Please bear with me!
LinkRank is an indicator of connectedness, reflecting how linked a page is. Given a "source pool" of webpages with hyperlinks and a "target space" of webpages, LinkRank is what you obtain when you order pages in the target space by their number of InboundLinks from the source pool.
LinkEcosystemServices such as Technorati often offer LinkRank lookup.
LinkRank is not the same as TrafficRank, because people who visit pages without linking to them don't contribute to LinkRank. A little-linked page may receive high traffic, though the two are generally correlated.
For instance, TechnoRati's source pool is the space of WebLogs, and it computes its NewsTalk index on the target space of news story pages and its Top 100 index on the target space of weblogs themselves.
Google computes a value called PageRank for the webpages it indexes. PageRank increases with inbound links, but it does not strictly map to LinkRank as described above because it does not value all inbound links equally. For Google the source pool is the same as the target space and it consists in the entire World Wide Web. PageRank as computed by Google is one important ingredient in evaluating the relevance of particular web pages.
DelIcioUs's popular links list also has the Web as target space, but it uses the set of del.icio.us linklogs as the source pool.
The exact extent of the source pool obviously largely determines what the results of LinkRank compilations will show. Take del.icio.us for instance. As I write this, a substantial proportion of users could be characterized as Web geeks, which obviously influences which links turn out to be the most popular. As the del.icio.us user base demographics evolve, however, the popular links will change as well. (This Discover article by Steven Johnson describes how the blogging population influences the content that shows up on Technorati Breaking News.)
It can be interesting to consider other source pools. For instance, I'd like an index that pools LinkLogs together with weblogs to determine popularity. Linklogging uptake has been crazy this year, with many non-bloggers taking it up and bloggers diverting some of their output to a separate linklog. At this time, there is probably as much relevance information in the aggregate output of linklogs as there is in blogspace.
Not everyone is interested in what everyone else has to say, however. You could for instance group del.icio.us users into niche subgroups (say, audiophiles) and effectively make mini-del.icio.us popular links lists taking only group members' linklogs into account.
The ultimate source pool might thus be a customized one for each user, one that answers "What's hot on my buddies' radars these days?" rather than "What are bloggers talking about these days?". Suppose you had some way of specifying a set of trusted sources (I've called that my microblogosphere) and could get a custom-fit tally of links out of that pool. The results would likely be more relevant to you, especially if you're somewhat eccentric with respect to the larger collective but have managed to find a number of LikeMinds among bloggers and linkloggers.
One practical way of specifying a trusted pool would be to start from a short list of personally selected sources, say a webfeed subscriptions list, and follow the links one or two degrees out to augment the pool. (A LinkEcosystemService such as TechnoRati could do that easily.)