Favourite House Rule
I've played with so many house rules and unofficial tweaks to the rules over the hears that it's hard to keep track of them.
A few that have really stood out to me have included:
In a Vampire: the Masquerade game, for every page of character background that a player gave for their character's backstory, the GM gave an extra freebie point for character generation. The GM ended up capping this amount to 10 extra freebie points when two of us tried to outdo each others "modern gothic elaborately worded masterpiece".
I've enjoyed games of Mage: the Ascension where all magick was considered coincidental unless the player mentioned game mechanisms and rules... in which case it immediately switched to vulgar magick. And earned an extra point of Paradox.
There was also a GM who ran with the idea that each character was given a metallic pirate coin, if you handed the coin to him during the session, you could automatically claim the highest roll possible on an action. But if you didn't have your coin, he could hand you a new coin an you'd automatically earn the worst result possible on the action when the coin was passed.
But one of my favourite ideas, when playing something with a simple roll resolution (D&D, Pathfinder, Cyberpunk, anything Palladium, etc.) is to apply a "Ghost/Echo"/"Otherkind" mechanism into the rolls. Instead of rolling one die (and applying modifiers) to see if you succeed, roll two dice simultaneously. The player then chooses one of the dice to modify for a success outcome as normal, the other die is used to determine if they have to give anything up in the process, or if they suffer any immediate blowback for their action (high roll = no problems, mid roll = minor problems, low roll = big problems). This gets needlessly complicated in games where there is already. "Yes, and..."/"Yes, but..." structure, but it's not intended for games like that. For those numerous other games with a simple pass/fail mechanism it adds a fun level of depth.