A few days ago, we reported on Google's clarification of hidden text and how not to get yourself penalized. This is part of an ongoing "Popular Picks" series in Google Groups and Matt Cutts has decided to clarify the nofollow tag as well.
Matt introduces his post by saying that he had an interview with Rand Fishkin, which we reported on, where he gave some insights into nofollow. But to be clear, let's review what he has added.
Matt says that if Googlebot can't access the page, don't try to pass PageRank to pages. A "sign in" link is a good example of what you should nofollow.
What are some appropriate ways to use the nofollow tag? One good example is the home page of expedia.com. If you visit that page, you'll see that the "Sign in" link is nofollow'ed. That's a great use of the tag: Googlebot isn't going to know how to sign into expedia.com, so why waste that PageRank on a page that wouldn't benefit users or convert any new visitors?
Personalized pages, too, won't work. He adds that a link like "My Itineraries" has no value to the Googlebot because they vary per user.
nofollow, then, is a tag you'd use if you don't want Google to crawl a link from your page. The links may exist elsewhere (and are followed), though, which means that you may actually see those links indexed.
So nofollow as a link attribute causes Google to drop those links out of our link graph. If you have a nofollow link from page A to page B, we won't crawl via page A's link to discover page B. Note that we may still find page B via other links around the web, though.
Forum discussion continues at Google Groups.