Michael Corleone (Al Pacino) tries to reconcile his relationship with Kay (Diane Keaton) while seeking redemption. Rival mobster Joey Zaza (Joe Mantegna) along with other mafia groups make attempts on Michael's life, while his nephew Vincent (Andy Garcia) kills Joey out of revenge.
Vincent eventually becomes the heir apparent to the Corleone family, because Michael's children, Mary and Anthony really want nothing to do with it.
After leaving an opera starring his son, in Italy, an hitman shoots Michael, but the bullet ends up going through his shoulder and into the chest of his daughter. Mary dies, while Vincent shoots back at the hitman and kills him.
Just before the credits roll, there's a shot of an old, broken Michael Corleone, alone but for a puppy. The orange he was throwing drops out of his hand, and he falls out of his chair, dead.
NOTE: Scott points out that, "All through the Godfather saga, any time someone has or is near an orange, that means he's going to get shot and/or maybe die. Don Corleone is buying oranges in Part 1 when Sollozzo's men try to kill him. When the Don does die in the garden with his grandson later in the movie, he's carving up an orange to make fake teeth to play with his grandson. The orange thing is maintained all the movies."
Thanks XOXOgrI44, massiveattack4life, David H and Scott!