Drahflow comments on Algorithms as Case Studies in Rationality - Less Wrong
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Algorithms I find useful that I didn't put in the article:
--Find decent solutions to packing problems by packing the largest items first, then going down in order of size
--Minimum-description-length ideas (no surprise to rationalists! Just occam's razor)
--Binary search (just for finding a page in a book, but still, learning the algorithm actually improved my speed at that task :p)
--Exploration vs exploitation trade-off in reinforcement learning (I can't say I'm systematic about it, but learning the concept made me aware that it is sometimes rational to take actions which seem suboptimal from what I know, just to see what happens)
My classical example for algorithms applicable to real life: Merge sort for sorting stacks of paper.