Simulations methods are increasingly used in theoretical and (especially) applied probability. Personally, I have used simulation for purposes that range from recreational Q&A to applications of considerable practical importance. Examples include (a) discovering that 'solutions' to combinatorial problems are clearly wrong, (b) checking the practical usefulness of bounds, and (c) multidimensional integration with MCMC methods where it seems simulation is the only feasible path to an answer.
For teaching simulation, I would very much like to have a collection of specific applications of probability simulation methods from people at various mathematical levels and in various areas of the mathematical and other sciences. Your personal accounts of specific, actual uses of probability simulation would be much appreciated. Some applications might be bootstrap, permutation test, MCMC, Gibbs sampling, Metropolis-Hastings, but many others. (I am not especially interested here in philosophical comments on the nature of randomness, the quality of PRNGs, or uses of software for exact probability computations that don't involve simulation--all perhaps useful discussion for another venue.)