Humans love tinkering with existing things. When talking about music, you can always find new ways to listen to a song... Some examples would be something like an "Isolated Track" where an instrument (or vocals) from a song are isolated and played on their own (like this example of Smells like Teen Spirit with Just Kurt Cobain's Vocals). We also figured out that playing songs backwards sounds like the devil, like in Stairway to Heaven by Led Zeppelin. (We'll come back to that song in a second). Theres also even people who can take an existing song and make every instrument play the same note for the whole time, like in this example of All Star by Smash Mouth that got re-tuned so
that the only note played and sung is C. I personally love going on the internet and listening to my favorite existing songs in different ways (Mostly using isolated tracks) but I do have a second favorite way.
In every song, there are instruments or vocals panned left and right. This means that they were intentionally moved to be more prominently heard in the left ear, or right ear. Some songs do it to add punch to something... Some songs do it to "fit" more instruments in. There's no set reason to do it, but every song does it.
Guns N Roses does something interesting with their mixing and panning... In the song Welcome To The Jungle, they put Slash on the right side, while Izzy sits on the left. Because each player plays different parts, if you listen to each side individually (with only one earbud in), you technically are listening to a different song that is "missing" a guitar player. Not that this is some massive difference or anything, and I'm probably the only person who thinks this is cool. I just think for me, it helps appreciate every little detail you hear that you might overlook otherwise.
Other songs like Stairway To Heaven do this as well, with the guitar on the left side and a flute on the right for the first few minutes. Bohemian Rhapsody does something too... in your right ear, you'll hear Freddie Mercury sing in an octave higher than in the left.
One song, however, does it better than them all. This song actually is two "different" songs played in each ear, but once you put both headphones in, it then becomes a third song.
It's actually crazy! Like the planning, the melodies, the vocals, all had to be thoroughly thought out to make sure it would still sound good together. It hurts my brain a little bit to listen to both sides together (I'm still unsure how I feel about when you combine the sides). Yes, I did listen to this song three times to be able to hear each "version."
If you have any more examples of songs that intentionally do this kind of thing, leave it in a comment! I'd love to hear them! I want to avoid songs that use a panning effect or binaural audio effect though. (Here's one that'll make you dizzy as a bonus) Let me know!
Some more honorable mentions from me would be:
When I'm 64 - Beatles
Wish You Were Here - Pink Floyd
The Whole Darkside of the Moon Album - Pink Floyd
Space Odyssey - David Bowie
Money For Nothing - Dire Straits
I Wanna Be Your Dog - The Stooges