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One of the leaders in the "smart people making smart tools" category, Wolfram Research are the makers of the computational software Mathematica, as well as the computational knowledge engine Wolfram Alpha. While the whole math thing makes me shudder, the idea of structured data is fascinating. The computational power of Mathematica is incredible (although, admittedly, it doesn't take a lot to impress me when it comes to math, Wolfram Alpha does know the correct answer to the query "What is the meaning of life?"), and the Wolfram Alpha API allows developers to build their own tools to hook to the technology.
My math phobia aside, a post on the Wolfram blog caught my eye yesterday: 25 Best Hangman Words. It's a very interesting look at how to solve a problem like "what's the best hangman word?" by way of an explanation of the Nash Equilibrium from math theory. (And I don't mind using math if it will help me win at word games.)
There are numerous Wolfram Alpha widgets you can install on your site, as well as just the search bar. And the Wolfram Alpha community forums have several discussions about how educators are incorporating the tool(s) into their curriculum.