Courage the Cowardly Dog follows Courage (Marty Grabstein), a pink and easily frightened dog. He was abandoned while a puppy after his parents were forcibly sent into outer space by a crazed veterinarian.[2] He lives in a house with a connected garage near the fictional town of Nowhere, Kansas with Muriel Bagge (Thea White), a friendly, sweet-natured Scottish woman, and her husband Eustace Bagge (Lionel G. Wilson episodes 1–33, Arthur Anderson episodes 34–52), a grumpy, greedy farmer who regularly mistreats Courage and refers to him as "stupid dog." Muriel found Courage in an alleyway and took him in as her own.

Courage, Muriel, and Eustace frequently encounter monsters, aliens, demons, mad scientists, zombies and other such perils from myths and legends. The plot generally uses conventions common to horror films. Although most of the creatures that the three face are hostile, some turn out to be friendly and are simply suffering from distress and acting in desperation.

The task of protecting the three main characters from such dangers falls on Courage, who endeavors to thwart or reconcile with the monster of the week and remedy or repair any damages done. Although Courage is occasionally aided with that task, the full extent of his efforts is usually performed unbeknownst to Muriel and Eustace. Ironically, given his name, Courage is a genuine coward, but still goes to great lengths to protect his owners.