Old Joe’s Place, by The Folksmen narrowly edges out Never Did No Wanderin’.
Regards,
Shodan
Nigel Tufnel that is. David St. Hubbins is the lead singer.
ETA- I love Deathklok.
U Stink But I Luv U, by Billy & the Boingers.
Shangri-La by The Rutles would be my favorite, though.
Another one for Big Bottom.
I’m probably gonna be pilloried for liking this movie, but, from Josie and the Pussycats:
Pretend to Be Nice and You Don’t See Me by the eponymous band, and Backdoor Lover by DuJour. (PtBN and YDSM are both good songs, BL is a very funny bit of parody.)
From Suicide Club, Write Once by Dessert, and Suicide Kiss, by Genesis.
The Tap’s got a good set to choose from, I’ll go off This Is Spinal Tap entirely and nominate two from Break Like the Wind - Majesty of Rock and Sun Never Sweats.
“On the Dark Side” by Eddie & The Cruisers (John Cafferty and the Beaver Brown Band)
“I’m a Believer” by the Monkees
“Love Comes and Goes” by Stillwater. I love the intro of this song in the movie “Almost Famous” and wish we could have heard the fake band sing it in its entirety. Nancy Wilson’s version is on the Director’s Cut DVD but not as intriguing as the live version.
Is Tenacious D too much of a real band to make this list? I have always LOVED “Kyle Quit the Band”
“Ice Froggy Frog” and “#$^^ the Security Guards” by NWH from the Fear of a Black Hat movie.
I was always partial to “Clearasil Messiah” by Deathtöngue. 
More than “Bitch School”?
And be jealous, I saw the Tap live for their Break Like the Wind tour.
I think I’d flip-flop those - but as far as A Mighty Wind goes, I got an even bigger laugh from the the title song.
As in, “I Wonder whatever happened to the Oh-nee-ders?”
From the Spinal Tap oeuvre, my personal favorite is “Stonehenge”. 'Tis a magic place, where the moon doth rise with a dragon’s face! 
Nah. I fell in love with them when they were on HBO, and consider them a fake band. Spinal Tap toured, right?
Immature as I am, I’ve always loved “Sex Supreme.” “Kyle Took a Bullet for Me” is awesome as well.
Joe
“The Flame Still Burns” - Strange Fruit (from the movie “Still Crazy”)
“We All Die Young” - Steel Dragon (from the movie “Rockstar”)
“Fever Dog” - Stillwater (“Almost Famous”)
I cannot get enough of Scotty Doesn’t Know from the movie Eurotrip. I like the song, and even more, remembering Matt Damon’s performance just cracks me up every time.
Another vote for various songs by The Rutles, though what with there being a touring cover band called Rutlemania, calling them a “fake band” is kind of borderline now.
I genuinely like (and not just for parodic value) the songs Blue Suede Schubert and Get Up and Go.
And from their follow-up album of songs not in the original movie, Eine Kleine Middleklasse Musik sounds like a song John Lennon would have been proud of, Questionnaire is almost more Pythonesque than Beatleseque, and Back In '64 is actually kind of touching and recalls George Harrison’s When We Was Fab as much as the Beatles’ song When I’m 64.
I prefer “Cheese and Onions” from “Yellow Submarine Sandwich”.
Freaky!! Outie!! from Home Movies 
I prefered “A gangsta’s life aint fun” (very nsfw), or “my peanuts”. I wish we could have heard “don’t shoot until you see the whites” though.
Most of the soundtrack from Starstruck, especially “Body and Soul,” “Temper, Temper,” “I Want to Live in a House,” and “Monkey in Me.”
The band was called “The Swingers,” and couldn’t they have come up with something just a tad more imaginative?