It’ll be extremely difficult to know if you’re running into patented mechanics or not (they are mercifully very rare), but some examples:
The use of a directional arrow indicator in the Crazy Taxi games.
‘Ghost’ cars in racing games.
The battle system found in Square’s JRPG games (aka ATB).
Microsoft have some absurd patents, whose descriptions are annoyingly broad, for example one describe where “Subjective style points are awarded if the player performs feats of style that are not necessary tasks of the game, depend upon the type of game, and may include sliding, spinning, jumping, blocking an opponent, passing an opponent, and avoiding obstacles.”