I am still a little early in my math education but we were talking about this the other day. Mine is the right angle proof of the derivatives of inverse trig functions. The first time I went threw them I was just given the rule that the derivative of arcsin is such and such, with no real explanation. It was hard to remember and didn't make a lot of sense but after I took the time to look at the very simple proof it all beautifully clicked together. What are yours?