A joke whose humor derives from repetition, ideally becoming funnier each time it is repeated. Must be repeated at least three times, otherwise it's a Brick Joke or Chekhov's Gag. But repeat it too many times and it can become an Overly-Long Gag. A variant is a joke that occurs Once an Episode; doing that too often threatens to turn it into an Overused Running Gag.
The ultimate fear for the use of any running gag is that it becomes an Overly-Long Gag, or worse, it was never funny in the first place and didn't improve through repetition. Nothing is worse than starting a one hour show with a joke that bombs that you're going to use twenty times over the next hour.
A Running Gag can be limited to a particular episode or recur throughout an entire series. If it recurs throughout an entire series, then it will often develop variations and/or be accompanied by Lampshade Hanging. If a character breaks the fourth wall to mention it, it's Didn't We Use This Joke Already?. When the story goes on to kill off the gag for good (either with a final payoff or just by referencing that it's become too overused and it's ending right then), that is Running Gagged.
A comedy Catchphrase is a type of Running Gag. Can become potential for Memetic Mutation if the gag itself is widely applicable. Compare Arc Words, which are a recurring phrase that isn't a gag. See subtropes Once per Episode and Every Episode Ending.
Running Gag has been suggested to play 6 roles. Click below to see other actors suggested for each role, and vote for who you think would play the role best.