My philosophical research has involved investigating the logical underpinnings of utility theory, in a manner influenced by John Harsanyi. One of the all-time great intellectual landmarks is Euclid's Elements, which amongst other achievements derived a whole system of plane geometry (parallel lines, circles, polygons...) by logical deduction from just five axioms. The principle of subjective expected utility similarly reduces a whole system of decision making (in an admittedly abstract realm) to a few axioms and could be argued to be an intellectual milestone of similar importance.
In studying the psychology of cognition and decision making, one reads large numbers of results on (mis)estimation of probabilities, context-dependency of preferences and so on. To evaluate these results (for example to ask if people really count as rational) one has to study the norms of probability and decision-making. (If you don't know the answer to the questions the experimenters are posing, how can you tell if subjects are getting them right or wrong?) Economic thinking is also necessary when we take an evolutionary perspective and ask what trade-offs are made by evolution in making human beings the way they are. Steven Pinker's survey of cognitive science, "How the Mind Works" is peppered throughout with applications of economic thinking to psychological questions.
My introduction to economics was Dixit and Nalebuff's delightfully fun and involving "Thinking Strategically" but for a more meaty textbook on the theory of rationality and how it bears on human psychology I swear by Johnathan Baron's "Thinking and Deciding". "Weighing Goods" by economist/ philosopher John Broome struck me as an extraordinarily careful and clear application of economic thinking to some deep issues.
This site was created as an illustration of how it is possible to create economics material for the Web, without fancy, flashy software. I hope that this site and its set of companion articles will eventually build into a complete beginner's guide to making academic Web sites. Some of the articles are linked below.