OK, so maybe it's not your favourite RPG, but there is that little rule you loved and made the system stand out for you.
I'll start with The One Ring RPG (TOR), the newest Tolkien's Middle Earth RPG from Cubicle 7.
There are many rules I love in there and the game currently stands as one of my favourite systems to date, but here's one rule that stood out at first read:
The game has Fatigue (kinda like encumbrance) and Endurance (kinda like hit points). As long as your current Endurance is above your Fatigue, you're fresh. If your Endurance is lowered below your Fatigue level, you become Weary, which brings penalties.
So the more equipment and wargear you carry, the quicker you get exhausted in combat (but you still don't get knocked out until your endurance is brought to 0). Thus the player has to balance weariness with protection from armour (which acts as a save to avoid getting wounded).
This Endurance/Fatigue relationship is echoed with Hope and Shadow, the later representing mental fatigue and the "burden" of evil on the soul. Hope can be spent to "boost" your rolls and trigger abilities, but when it drops below your current shadow score, you become Miserable which also brings penalties (and put you at the risk of going all Boromir on your Frodo companions).
So what are your favourite game mechanics?