I appreciate the sentiment that you shouldn't memorize theorems, but I think it goes too far. Some theorems are just not that memorable. You can prove them over and over and they don't stick. And if you use a theorem repeatedly, it's worthwhile to memorize it so that you won't have to interrupt the flow of your thought to look up or derive the result.
Diagrams sometimes help. For example, here's a diagram of relationships between probability distributions that I've often referred to. And here's a diagram relating various modes of convergence.
