The Legend of Zelda Majora's Masks' 3 day cycling. It's not even something worth describing nor something that could be shown off in a GIF as one only truly appreciates it by playing the game and ultimately playing the system. It impacts everything from the gameplay, the atmosphere, the story, the characters, the setting everything. It's absolutely genius.
EDIT: damn beaten.
Ah well other that come to mind that I really like are Splatoon's movement mechanics, BoTW's climbing, Bloodborne's rally system, Xenoblade Chronicles' chain attacks, Xenoblade Chronicles X's Skells, DOOM (2016) gory kills, Chrono Trigger's time travel, Earthbound/Mother 3's rolling health system, needing to stop moving to aim in Resident Evil 4, Brave/Default system in Bravely Default, mercy option in every fight in Undertale.