Many years ago, when I first started in the search marketing industry, several instances of the debate around "themed links" flared up, cooled off and reared their head again. Nowadays, it makes infrequent, though periodic appearances in the thinking, recommendations and forums of the SEO world, and I thought it would be wise to revist the issue, lay out the discussion points and get folks talking about their experiences, tests and intuition.
The basic tenant of the themed links debate revolves around the theory that search engines run calculations to identify "neighborhoods" of topically-related content, and then consider links from sites/pages on these topics to be more important or valuable than those from unrelated neighborhoods. Here's a visual take:
While personally, I've seen little evidence that an algorithm like this exists at Google, Yahoo! or MSN/Live (haven't honestly done enough Bing investigation to feel confident making statements around their practices), I'm very curious to hear your thoughts._
Let's open this up in the comments - do you think themed links matter? Can you do well without them? Is there reverse-theming (where links from outside your neighborhood or from diverse neighboorhoods provide more benefit)?
p.s. For more on the origins of this theory, see Authoritative Sources in a Hyperlinked Environment by Jon Kleinberg (warning PDF) and notes on the HITS algorithm lecture from the Math Explorer's Club at Cornell University.