First of all, before Sergey Brin or Larry Page even learned the word 'algorithm', there were web sites that practiced the fine art of reciprocal linking. Pre-Google link exchanges served only one purpose and that was to develop direct traffic from those links. This still works! Somewhere in our PR worries and link popularity ambitions, we forgot one important fact: you never know when the next link you obtain for your site will be a direct traffic producer. For example moving.ca, provides daily traffic to www.abalone.ca through a small, text link on their links page. This does not come up on Google as an incoming link to Abalone Designs, but it is one our most valuable incoming links, nonetheless.
Now, as far as your ranking is concerned on Google, links still hold weight. Search for just about any term or phrase and check the #1 ranked site's incoming links versus the others. 9 times out of 10, The first ranked site will have a few more links than the others. The times when I see lower ranked sites having more incoming links than the #1 site, generally speaking, the #1 site has better content, and more of it or this site's incoming links have anchor text that contain the exact search term or phrase you searched for and the others don't. It's still the same old formula. Offer a content-rich, user-friendly site with incoming links that have relevant anchor text and your site will do all right.
Relevant anchor text is important, but what about having your link on relevant sites? Links on relevant sites or pages have one tremendous bonus and that is targeted traffic. This is providing, of course, the link produces direct traffic. Other than that, I say links on relevant pages aren't that much more important than other links.
Take, for example, the incoming links to seoinc.com - the very first page that shows up on Google when you search for seoinc.com's incoming links, is csmonitor.com. A Christian Science magazine! If I'm missing some link between religion and SEO, please inform me, but otherwise, these two sites couldn't be more different. Google has deemed this an important incoming link for seoinc.com, regardless. You think you know the algorithm, but you don't. You never know when links will count.
Let's not forget about the other search engines, though. Still a few steps behind Google, MSN places a lot of weight on incoming links. So does HotBot, Yahoo! and now, apparently, Become.com. This is just a handful of places that take a critical look at your link popularity. And I hate to say it kids, but I think there's a chance that MSN might slightly outdo Google this year.
As of late, I've noticed different rankings on Google for clients based on where you're searching from - geographically-specific search results against our will. I haven't spoken to one individual who likes this idea. This could be the giant mistake MSN has been waiting for Google to make, and you don't want your perfectly Google-optimized site to miss the MSN bus when it's usage tops Google's.
This brings me to my last point which, quite frankly, is a no-brainer. The Internet is nothing but a massive network of links, hence 'net'. To turn your back on this is one of the hugest mistakes you can make on the web. The more links you have around the web, the more often your site will be seen. It's just like the real world, "there's no such thing as bad publicity". Think of incoming links as cyber-publicity - there's no such thing as a bad incoming link.