In fact, links pages themselves are a particularly bad idea, unless they are in context (a corporate partners page, for example).
In the thread, a few posters encourage editing the links directory, leaving only those links that are relevant. Ensuring the links are relevant to your visitors is kind of obvious, but what nobody seems to have touched upon is whether they are actually useful.
If you have a site about widgets then a links page listing other sites that focus on widgets would seem like a logical move, but would it be useful to your visitors? Lists of links is a very blind way of exploring the web, hence why the search engines stole market share from the directories so well.
Much better is to have links to relevant sites in a contextual way, where it makes sense. For example, on a page about custom widgets, links to custom widget manufacturers or examples of custom widgets can be included within the normal flow of content. The links are likely to be much more helpful to the visitors when presented this way.
A couple of posters in the thread talk about a quota for reciprocal links versus one-way links. Using such a system is also a bad idea. The only way links can be completely natural (and therefore arouse no suspicion from the search engines) is to be measured entirely qualitiatively. Using a quota is an attempt at using a single quantative target to match an algorithm that looks at numerous qualitiative and quantitative factors.
If you have a links page, think about whether those links serve the needs of your visitors. If they do, think about how they could be incorporated into the content throughout the site to better serve those needs. Then do what makes the most sense and forget about search engines!