In Black Rose, it's possible to kill Polly by mashing the Fire button repeatedly. The game actually rewards you with 2 million points for doing so!
One of the central elements of the Metallica pinball table is Sparky, a guy hooked up to an electric chair. Electrocuting Sparky is needed to activate certain modes, and one of the end-of-ball bonuses is based on how many times you've electrocute him. Furthermore, electrocuting Sparky seven times during a single ball lights all shots for a Super Jackpot.
Mick Jagger will move back and forth about halfway up the playfield and get in the way of shots you want to make in The Rolling Stones. In order to make those shots, you have to bash him with the ball to make him move out of the way. It's an unusual design choice to make The Rolling Stones fans beat up Mick, but it is perhaps satisfying for those who dislike him.
Star Wars Episode I has the required mode "Jar Jar Juggling," where the player is asked to make Jar Jar Binks trip and take the objects he was juggling.
When White Water's "Man Overboard" activates, most experienced players choose not to save him and just watch him flailing away down the river until time runs out, upon which he presumably drowns. This is because they don't want to risk losing the ball for a relatively small reward, and there is no penalty for failing "Man Overboard."