Even if it didn’t have grooves as such (cassette, CD, whatever), did you play it well past the point of memorizing every note?
I had several I played that much, but the one that comes to mind quickest is The Music from Peter Gunn.
Every Picture Tells a Story=Rod Stewart
Bat Out of Hell-Meatloaf
Bat Out of Hell as well.
Back in Black - AC/DC
Side 4 of Electric Ladyland. (I assume you mean literally wore out the grooves, 'cause that’s what happened - the needle would slip out of them near the end and slide across the record!)
Yep, that’s the sort of thing I meant. Polished slick even. Did you have to get a replacement copy? There are maybe 20 albums I have had on vinyl, cassette, CD and on YouTube. That’s my “desert island” group.
Prince, Purple Rain
Paranoid by Black Sabbath.
Shout At The Devil - Motley Crue (sorry not doing the umlauts).
There were many (high school was like that), but my most egregious case of obsessive listening has to be Jesus Christ Superstar. Two LPs!
The only time I actually saw the grooves worn out on a record was at my college radio station for John Mayall’s “Room to Move.”
Prince “Purple Rain”
Saga “Worlds Apart”
Soft Cell “Non-stop Erotic Cabaret.”
I listen the hell out of Led Zeppelin IV
To bring a slightly different flavor to the proceedings:
My Name is Barbra, 1965 I believe. It was the first LP I ever owned. I saw the TV special first, then I had to have it.
This is one area, anyway, where I fit the stereotype completely.
Roddy
I wore out a copy of “The Turning Point”, the album that song is on.
Another one for Purple Rain. Also, from the same year, Let It Be by The Replacements and Zen Arcade by Husker Du. I literally wore out my records/cassettes of these. Guess I had a lot of free time when I was 14.
Songs from the Big Chair, Tears for Fears.
Speaking in Tongues-Talking Heads. I listened to it so much that I knew the words to every song.
1969 -Good Morning Starshine album by Oliver. 
Wasn’t in high school yet but that was the first album I bought and played till it wouldn’t play no more.
The very first album I ever owned was Telstar by the Ventures.
It was the background music in my bedroom for the entirety of the 1966 and the better part of 1967 until the needle started skipping.
Poe Hello did not leave my cassette player until I had to replace it with another copy. It was the same with Less Than Jake Losing Streak.