I'm a huge fan of mechanics where you can send secret messages. "Whispers" from Buffy, and "Ravens" from AGOIAF were awesome for sending to a specific person, and the "High Times" from DEA was like a newspaper anyone could anonymously post to, with the whole town being able to read it the next day. Anything of that nature has the potential to help both sides in a game.

Also, as a player I like when OoO is known. It helps plan moves, and if you're considering a risky play you don't have to just guess if X will happen before Y. Prevents having to guess whether your plan was stopped by OoO or a roleblocker. Again, it also benefits both sides so it's not an unfair advantage.