I first encountered Bayes Theorem when I studied probability theory in high school, and until recently thought it was just another formula. Useful to solve puzzles, perhaps, but not the most elegant mathematical formula I've encountered.
Over the past year, I have been reading up on a lot of recent technical literature on Bayesian analysis, particularly as it pertains to solving important inverse problems using Markov chain Monte Carlo methods, and have been experiencing something like a muted, but prolonged epiphany.
Bayesian thinking is very under-emphasized in Math curricula (or maybe I just wasn't paying enough attention). This is particularly sorry since being able to tease apart statistics that get thrown at you has become a necessary tool in any survival kit. Here is a link to a great, gentle introduction for an interested, but uninitiated reader.