Bart starts a Bank Run, just like in It's a Wonderful Life! "It's in Bill's house and Fred's house"
In "Miracle on Evergreen Terrace", the last scene in the film is once again played out when the townspeople bring money to the Simpsons when their gifts and tree are "stolen." The film is further spoofed when Homer tells Lisa to stop playing the piano, which parodies a similar scene involving George Bailey.
In "The Last Temptation of Homer", Homer is visited by an angel disguised as Isaac Newton to show Homer what his life would be like without Marge. In the film James Stewart's character is also visited by an angel disguised as Newton to show him what his life would be like if he committed suicide. The ghost in It's a Wonderful Life is Clarence, Angel Second Class, working to get his wings. Newton is not a factor.
In the episode "Grift of the Magi", Moe Szyslak gives the Simpsons a plump Christmas goose after having a dream where he saw what the world would be like if he never existed. (This also references the film/novel A Christmas Carol.)