Come Back, My Pet

An owner and their pet have a falling out, where the owner either replaces the pet or shoos it away. Then circumstances happen where the owner needs their pet back or is in danger, and only their pet can rescue them. They reconcile, and the statue quo is returned. This is not limited to standard pets like dogs or cats, by the way; even a tiny creature like a termite can fit the bill if they are treated like a pet -- that is, cared for and nurtured, with a genuine bond.

Compare with Timmy in a Well, when the pet and owner weren't separated before the human gets into trouble; Androcles' Lion, where the animal isn't a pet and they weren't together to begin with; and Tropey Come Home, where the separation is involuntary.

Comic Books

 * A Goof Troop comic in which Pete replaces his dog with a cardboard robot guard dog after their house gets robbed. Turns out "Card" is actually programmed to let its creator in to rob the house again.

Film

 * In Lilo & Stitch, Lilo tells Stitch to go away after she discovers that he's an alien, and that he's the reason that they were being pursued by Jumba and Pleakley. Right after, however, she gets captured by Gantu, and Stitch rescues her.

Literature

 * In the Hans Christian Andersen tale "The Nightingale", the Emperor of China tames a nightingale, but neglects it in favor of a clockwork bird. When Death comes for the Emperor, it is the live Nightingale who charms the Grim Reaper with his sweet song.

Western Animation

 * Courage the Cowardly Dog: Courage routinely does this for Eustace, who routinely scares and abuses him. However, it's less out of the goodness of his heart and more because of his devotion for Eustace's wife Muriel.
 * In a Tom and Jerry cartoon, Tom's owner gets annoyed that Tom never tries to catch Jerry anymore so replaces him with a robot mouse catcher and Tom is kicked out. Since Jerry can't live in the house due to the robot throwing him out he and Tom work together and eventually the robot goes wild and Tom rescues his owner.