Declining to reveal my previous salary when negotiating a new job. I ended up with a significantly better salary than they originally offered and never even said a number. Just built a good rapport with the hiring HR rep and agreed that the offered amount would be totally reasonable for [someone else with good experience]. Then I pointed out that I also bring to the role [additional, relevant, and desired experience]…
I reckon if you don't do negotiation on a regular basis, learning to keep your mouth shut, as this post says, is the single best and easiest thing you can do to improve your outcomes. When you ask your question (this one is great btw - what can you do to make that number better), the other side may, subconsciously or (for more experienced negotiators) consciously just say nothing for a while. They're waiting for you…
When buying used cars, I will often just ask, "Is there anything else I should know about the car?" and then wait.
It's also good for extracting confessions ("What can you tell me about this broken cookie jar, son? [long pause]").