Hi Carl,
Dana has a brilliant answer here, but I'll add a couple more things:
Links are still a heavy part of the ranking algorithm, but it's absolutely clear that Google wants to move away from this reliance, simply because link building has been scaled so effectively by so many people that it is not a true measure of impartial authority anymore. I'm sure they would love to rely on social signals as this is people talking about what they like, don't like and do in a candid fashion, but Google doesn't have the ability to infiltrate the most valuable social network for this (Facebook) yet, and they probably never will.
As such, they still need to rely on what is posted on the rest of the web, and citations / "mentions" seems a good place to start. It has long been true that they seem to look at "links" that are not link but simply cited URLs (e.g. if I write out http://www.site.com/, this CMS doesn't link to it but Google crawls this page and sees the URL). This is plainly obvious if you are checking a site's 404 errors through Webmaster Tools - I have seen a lot of "404s" that aren't links: Google reports a broken link in WMT and shows you where the link is placed on the third party site; you visit that site and see that it is not a link, but simply a URL written out like the example here.
Does PageRank pass "through" that "link"? Impossible to tell exactly how Google deals with those from an authority point of view, but they see it. And they would clearly be wrong to ignore data like this, so we can expect that such citations are at least factored into how a site appears to Google.
It's also likely that they take into account mentions of a brand name in a similar way, and links that are nofollowed. It's impossible to say how, but I would certainly like to guess that 100 mentions from authoritative sources (including many newspapers that do not link out, as a rule) are more likely to increase a site's authority than 100 links from questionable or lower-quality sources.