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In a number of ways, including some that were good for people who never used the Google Directory. The most obvious way they were useful is that it allowed people to click on the directory link to find other sites similar to the one in the SERP. This tended to be useful for non-commercial informational sites. Quite often the very good ones are poorly SEOed (non-commercial webmasters tend not to worry much about SEO), and thus they rank poorly in the Google SERPs. However, the most authorative info sites on a topic usually will be listed in the ODP.
The directory links were also useful to people who didn't care to use the directory in that they could be used to spot sites that the searcher likely wouldn't be interested in. For example, if someone wanted to buy a widget and entered "widgets" into Google, if a site on page 1 had a link to an ODP category that was obviously non-commercial, this likely would be a site to avoid. As in if the site is in Widgets > History or Widgets > Safe_Use, rather than Shopping > Widgets, it probably isn't the best place to look to buy a widget at the lowest price. One problem for those looking to buy something is that the PageRank aspect of the Google algo tends to favor non-commercial sites, and make them more likely to rank high. Non-commercial sites tend to link to each other, bulding up PageRank. E-commerce sites for obvious reasons tend not to want to link to the competition.
... for finding the Category that all the similar sites were in; rather than continuing through the search results I would jump to the category instead.
... for spotting high-ranking sits that were not already included in the directory, and then adding them in if the content merited it. Neighbouring sites in the search results also showed which categories that the other similar sites were already listed in.