Michigan J. Frog was originally a one-shot character in the original Looney Tunes series. But his one cartoon turned out to be a highlight of American Animation, resulting in frequent cameos, revivals, etc over the following decades.
His original cartoon was "One Froggy Evening" (1955) by Chuck Jones. The story begins with your average construction crew worker getting involved in the demolition of the J. C. Wilber Building. He finds the cornerstone of the building and within it a frog. Which sings a dances to old tunes. A document inside the cornerstone indicates that the frog was buried there back in 1892. It doesn't matter to this working man.
What matters is an opportunity to get rich, by becoming the impresario of the frog. But there is one key problem. The frog only performs for him. Never for an audience. Which the guy realizes only after spending his entire fortune for promoting the act and renting a theater. The man ends up homeless with the frog by his side. His continued claims about the frog next land him to a psychiatric hospital. With the frog singing to him wherever they are alone.
By the time of his release the guy hates the frog. He approaches the construction site of the new "Tregowerth Brown Building" and hides the frog in the cornerstone. Feeling free at last. The scene shifts to the far future. In 2056, the the Brown Building is being demolished. One of the workers discovers the still living frog. He decides to become the impresario of the frog. The cartoon ends with the implication that the process never ends.
Michigan J. Frog is immortal. He doesn't need air, food or water to survive. His initial cartoon had him survive from the 19th to the 21st century with no sign of aging or fatigue. The sequel "Another Froggy Evening" reveals that the frog has been alive since the Stone Age.