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This might be a strange subject, but I feel like designers often have pet mechanics, quirks, or favorite little design tidbits that they are attached to. Here's my list, feel free to post your own in the comments.
One Hit Kills - instagib, the AWP, hammer item in Smash Bros., many an old school arcade game where you die in one attack from everything in the game (SHMUPS for obvious example)
Rolls/Dodges - in any 3rd person game where the character can roll to dodge attacks/falling boulders/lightning bolts (God of War, Zelda, God Hand, etc.)
Game Turn/Time/Round Structures - partially turn-based, partially real time games, or games that fit somehow in between the two categories.
Samurai Kirby minigame - a minigame from Kirby Superstar which is a randomly timed light-flash reaction test, which can be played PVP or PVCPU.
Physicalizing games - making games where physical interactions between pieces/participants determine the outcome. pinball is a good example of a physical interaction (ball and flippers)
Tri-stat systems - RPGs where there are three stats (the minimum? interesting number) rather than 6 or however many.