“Dancing With Joey Ramone” by Amy Rigby is also pretty good.
Superstar - the Carpenter’s version is not the original but by far the most poignant exploration of infatuated fandom. A classic take.
[For comparison - Delaney and Bonney’s original - titled as ‘Groupie’, and a modern take by Sonic Youth]
I’m shocked that we’re nearly at two dozen and its not come up.
I said, “I want to be a singer like Lou Reed”
“I like Lou Reed” she said, sticking her tongue in my ear
Been Tired Pixies
I was coming in with the Sleater-Kinney cut already referenced, so I guess I will pivot to Brian Eno. King’s Lead Hat, an anagram for his then new creative partners Talking Heads (aka the referenced ‘Four Turkeys in a Big Black Car’ 
):
The Knitters (the band X with Dave Alvin replacing Billy Zoom as a folk/country band) references the Rhythm Pigs in the intro to their cover of Rock Island Line.
Indeed. My favorite:
Another song about an Elvis fan:
One of my all-time favorite bands…just saw X opening for the Psychedelic Furs a couple of months ago. My sixth time seeng them live, if you count two Knitters shows. In their classic “I Must Not Think Bad Thoughts” they give a shoutout to a bunch of their musical contemporaries:
"I hear the radio is finally gonna play new music
You know, the British invasion"
But what about the Minutemen
Flesh Eaters, DOA
Big Boys and the Black Flag?
Will the last American band to get played on the radio
Please bring the flag?
Sara Borges’ “Same Old 45” is about a woman obsessed with “Brandy,” by Looking Glass.
And you know I shed a tear for him
As this ship was setting sail.
Sittin’ in my room playing the same old 45.
About a girl named Brandy, the would-be sailor’s bride.
So did I, and the Smokin’ Popes’ “You Spoke to Me” came to mind.
I drove all the way from Carpentersville*
To see you here tonight
And it was worth it
You didn’t play my favorite song
But that’s all right
I love the new stuff too
I’m just glad I got to see you
*A distant suburb which would indeed be a long drive home for a fan seeing the Popes in a typical Chicago club.
Does it have to be a fan of a musician/musical group? Because the first song that occurred to me is “Sally Simpson” from Tommy.
ninja’d while digging up the video!
Rollers Show / Nick Lowe
The Hoodoo Gurus [Australian band] tell you about all their fave songs and bands:
Let’s All Turn On
There’s a great song by German singer Adel Tawil called “Lieder” (“Songs”) in which he references famous songs by the likes of Michael Jackson, Whitney Houston, the Prodigy, EMF, David Bowie, the Bangles, Prince, Depeche Mode, Rage Against The Machine, Beck, Nirvana etc. etc.
My first thought was We’re An American Band
I heard “Killing Me Softly With His Song”, the famous Roberta Flack version, today on the radio and was reminded of this thread. The original singer and probable co-songwriter, Lori Lieberman (there was a dispute about songwriting credits between her and her producers, a typical story for the times), had the idea for the song when attending a Don McLean concert because she was so moved by his performance of “Empty Chairs”.
The whole story on Wiki:
My immediate thought: White Man In The Hammersmith Palais by The Clash. A disillusioned fan, but a fan nonetheless.
j