Usually bugs, glitches, and exploits degrade the experience of a game, but occasionally they can actually work to a game's benefit. In some cases, they can become significant enough to become part of a game's identity. In others, they make a broken game worth playing in the first place. Even without such legendary status, a given wrinkle in a game might simply make it more enjoyable or entertaining, or perhaps open up unexpected modes or paths of play.
What are some examples of these, and how did they improve their associated games?