Homer Simpson in: "Kidney Trouble"

Homer decides to take Marge and the kids down to Bloodbath Gulch, a ghost town turned tourist destination. On their way there, Homer's car breaks down, right in front of the Springfield Retirement Castle, leaving Grampa to assume that they've come to visit him on his birthday. Homer tries his hardest to start the car up again, but is eventually forced to take Grampa with them. While in the town bar, Grampa drinks too much sarsaparilla and just as the family is leaving, says he needs to go to the bathroom. Homer refuses to stop, saying that he needs to get home in time to watch Inside the Actor's Studio. Grampa is forced hold it in for hours and as a result, his kidneys explode (it should be of note that, in reality, Grampa's bladder would have ruptured from "holding it in"). Dr. Hibbert informs the family that Grampa doesn't have much time to live, and that the only way he can be saved is if Homer donates one of his kidneys. Homer happily agrees, and is admired and pampered for it by his wife and kids. However, he becomes frightened after finding out about the risks involved in the operation and, while he makes it to the hospital, jumps out a window at the last minute.
Guilt-ridden and ashamed, Homer deems himself unworthy of living amongst civilized people and decides to start a new life at sea, climbing aboard the Sea Captain's ship, described as 'the ship of lost souls' (in actuality, named 'Honeybunch'). While there, he meets several strange people, who have their own tales of misery. After Homer tells them how he ran away and left his father to die, they are angered and disgusted and throw him into the ocean. Homer eventually drifts back to shore, where he witnesses a father and son build a sand castle and laments how he never had such a relationship with his own father or his kids. Homer decides determinedly to rectify his mistake and takes off for the hospital.

Homer arrives in time, reconciling with Grampa and apologizing for his behaviour, but ultimately he panics and flees again when Dr. Hibbert says '...this may sting a little'. Homer's mad dash from the hospital is stopped by an oncoming truck. While the driver manages to hit the brakes at the right moment, one of the cars it was carrying slides off and lands on Homer.
Homer later wakes up in the hospital, covered entirely in bandages, and is greeted by Dr.Hibbert, Marge and the kids. Believing Grampa is dead, Homer sadly vows to visit his grave after he gets better. However Grampa, who is alive and well, appears in the doorway and declares that he's never felt better. Off the sheepish look of the others in the room, Homer looks down and discovers that, while he was unconscious, they took out one of his kidneys. Angry at first, Homer vows to get it back, but settles down after his family tells him that he did a good job. They engage in a group hug, and Homer proceeds to consider Bart as a potential donor for himself.

[edit] Cultural references

The scene in which Grampa approaches the car in front of the Retirement Castle is a spoof of the cemetery scene from Night of the Living Dead.
Someone says over the hospital intercom "Dr. Bombay, Come Right Away", a nod to the TV show Bewitched.
Hospital intercom System: "Doc Martens to Podiatry"
The first scene parodies the 1973 film Westworld.
When Homer is trying to read a liability form that requires his signature, the nurse says "Don't read it, sign it" in the same way that the prison guard says this to Alex in the 1971 film A Clockwork Orange.
The 'lost soul' in the tuxedo aboard The Honeybunch seems to be a reference to the actor Peter Lorre.

Apes-A-Poppin, one of the movies Bart rents for Homer the day before his first scheduled surgery, refers to the 1938 Olsen and Johnson Broadway show Hellzapoppin'.
When Lisa asks why they don't have another kidney to give to Grampa, Dr. Hibbert says that "Larry Hagman took it." In 1995, Hagman (who later guest voiced in the episode The Monkey Suit) underwent liver transplant surgery.