Ever since templates were added to Wikipedia, many people have thought about ways to make all the exciting data from the various infobox templates added to articles searchable in some way. DBPedia has done it: they have converted all the template data into RDF and made it browsable and searchable. Using, for example, the Leipzig Query Builder, you can ask questions like “which film composers were born before 1965″ or “which soccer player with tricot number >11 from club with stadium with >40000 seats has scored more than 100 goals”.
Of course, it is desirable to store this data in a structured form in the first place, and to make it searchable in real-time. This is what Semantic MediaWiki and OmegaWiki are aiming for, using different strategies (one provides you with a syntax to annotate wiki pages and stores all annotations in a machine-readable fashion; the other focuses only on the structured data itself and treats it separately from a wiki page). I believe that, after we’ve made some progress on quality annotation (priority number 1), adding content structure to Wikipedia should very much be the next priority for the Wikimedia Foundation.