When I'm browsing about randomly, it'd be nice to visit SO or one of the other StackExchange sites and have a more interesting set of recommendations. For instance, "questions I might be suited to answer" is not the same thing as simply "tags I've picked out". The same goes for "questions and associated answers that I'm likely to learn something from". I think either or both of these could dramatically increase participation. I recognize that they're both fairly substantial increments of functionality, though.
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Do you have any sort of specific suggestion as to what this would do or how it would work?
The site already
so I'm not sure what else you're suggesting short of mind reading. If you want another way to get exposed to new stuff, lately I've been finding it when reviewing. You'll see all sorts of topics, and you can clean house at the same time.
I would use a recommendation engine, similar to Amazon's. It would be based on a machine learning algorithm, that tries to "predict" my behavior, based on a set of features, e.g. the tags that I visit often, the text of the questions that I click on while using SO. One could train the algorithm by comparing the predicted behavior against the actual behavior of a user.