A (board) game that I think has excellent disruptive events (There are probably quite a few) is the Game of thrones board game. Every turn (except the first), three event cards are drawn that might throw off your plans for the coming turn completely. A game-winning strategy set up on the previous turn can be undone by the rain event card for instance, which can limit you to two march orders on the coming turn (instead of three). This functions by, as hexgrid formulated it, limiting your capabilities. It becomes a big deal (disruption), without it being a case of "you just lost the game because the wrong card came up".
PS: the Star Trek episode is scheduled for ep250 if I recall correctly, someone listening to old episodes will have to confirm.