In Sherlock Holmes Nemesis, the player, as Holmes, must have his companion Watson with him, of course. Unfortunately (or hilariously), instead of simply having Watson walk behind you, the game engine never has him actually move. Instead, he simply appears to soundlessly teleport right back next to you whenever you're not looking. A hilarious youtube video illustrates the problem.
Infocom games, being text-based, have some of the most amusing glitches in gaming, as your mind can fill in ridiculous blanks to make them seem more ridiculous. Some gems include poking the idiot in Arthur: Quest for Excalibur, causing him to drop dead and losing you the game, giving robotic commands, even suicidal ones, to the humans trying to kill you in Suspended, and throwing body parts, like your hands or head, across the room in Plundered Hearts, leaving them lying there on the ground where you can't retrieve them.