You can find much of the references in the game's famous (infamous?) soundtrack.
Part of the reason why Earthbound has been having difficulty reaching Western shores again is POSSIBLY because so much of the music is taken from popular bands, especially The Beatles.
Instead of telling you about the specifics, you can listen to the tunes yourself. Watch the videos in both links to get a good idea of what has influenced Earthbound's music.
OTHER music references you can find scattered throughout the game.
In Onett, there's a man who'll ask you to fill in the blanks to name this famous Beatles song: "XXXterday." Your options are Yes and No.
Inside Dungeon Man, there's a yellow submarine, another Beatles reference.
In the Japanese version of Earthbound, default names you can choose from when you begin a game feature The Beatles.
Ness: John
Paula: Yoko
Jeff: Paul
Poo: George
Dog: Ringo
Favorite Food: Honey Pie
Favorite Thing: Love
Also in the Japanese version, the area called Peaceful Rest Valley is known as Grateful Dead Valley, named after the band.
Again, in the Japanese version, the Runaway Five, known as the Tonzura Brothers, wear black, making them look even more like the Blues Brothers.
They also wear black in their Super Smash Bros. Brawl appearance.