The following is a list of all board game mechanics I know in this category, and that aren’t too niche. Card game mechanics are also included. I’m posting this mainly for my own reference.

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Catch the Leader: The game systems advantage players that are behind or disadvantage players that are ahead.

Hot Potato: A single item is bad for players to have, and players strive to pass it to other players or avoid it so they are not holding it at game end or some other defined time. Example games include Old Maid, Exploding Kittens, and Catch Phrase!.

Lose a Turn: This is a meta-mechanism that can be applied to a variety of turn structures. A player who “Loses a Turn” must skip their next opportunity for a turn, and will go to the next round, or the next time their turn arises.

Once-Per-Game Abilities: Players have a special ability that they can use one time per game. These may be unique to them, like ‘feats’ in Warmachine, or common to all players, like the special power chits in Finca. Often players will receive bonus Victory Points if they do not use their one-time abilities during the game.

Player Elimination: A player can be removed from the game, no longer participating.

In some such games, all of an eliminated player’s material is removed from the game as well; in other such games this material may remain in play as neutral material. (E.g. an eliminated player’s armies and cities on a map might disappear, or might be become neutral armies and cities.)

In most games, an eliminated player cannot win, but this is not necessarily true. (E.g. in some games with victory based on scores, an eliminated player’s score is still eligible for victory.)

In most games with player elimination, a player is eliminated involuntarily. But in some games a player can choose to drop out (with hope that their score suffices to win (e.g. Wooly Wars).

In some games, player elimination is possible, but rare in practice and does not happen in a “typical session” (e.g. Age of Steam).

In some games, player elimination is common. In the extreme case, all players but one (the sole surviver = eventual winner) are eliminated during a session (e.g. Titan). In many player elimination games, typically some players are eliminated but multiple other players are not (e.g. Werewolf and BANG!).

Player elimination does not include two-player-only games where the goal is to defeat the opponent, e.g., Chess.