that's cheating!

Didn't Teenage Fanclub drop band names into virtually every song they wrote?

Public Enemy - BRING THE NOISE (mentions run dmc, yoko ono, anthrax, etc.)

I know

Hot Wire My Heart

sonic youth - mariah carey and the arthur doyle hand cream

Aw you beat me to it.

You'll Dance To Anything - Dead Milkmen

John Lennon sings 'I don't believe in Beatles' in the song God

ive been tired by pixies
what you need by the fall
i am damo suzuki by the fall
pennyroyal tea by nirvana

Fun Fun Fun-the Big Boys (Public Image Ltd, Joy Division)
Daft Punk is Playing at My House-Lcd Soundsystem (terrible song)
Screaming Skull-Sonic Youth
Unseen Power of the Picket Fence-Pavement (REM)
Since I've been your Man-Matthew Good (Led Zeppelin)
Born Losers-Matthew Good (New Order)

Daft Punk - Teachers

but there must be a million songs that mention other bands/musicians in the lyrics, so I'm not going to search further... now, a mention of another band/musician in the title of the song, I can't think of anything at the moment...

bo diddley by bo diddley

LCD Soundsystem - Daft Punk Is Playing At My House

A lot of Fall songs

CSS - Let's Make Love And Listen To Death From Above
Liars - Tumbling Walls Buried Me In Debris With ESG (okay it uses an ESG sample)

Gil Scot Heron- The Revolution Will Not Be Televised (Johnny Cash, Engelbert Humperdink, a few others)
Dr. Octagon- I'm Destructive (def leppard, Van Halen, Grateful Dead)

Sleater Kinney- I wanna be yr Joey Ramone (Thurston Moore in 2nd chorus)

Clash- 1977. No elvis, beatles or the rolling stones.

U2- Angel of Harlem- lots. Lady Day, Miles, Coltrane, etc

Billy Bragg- Levi Stubb's Tears

"James Brown is Dead"

Dead Milkmen- Punk Rock Girl. Mojo Nixon

Minutemen- Bob Dylan Wrote Propoganda Songs, Political Song for Michael Jackson to Sing

Eminem- "Will Smith don't have to cuss in his songs/But I do."

Public Enemy- "Elvis was a hero."

One of the most immediately obvious is Unseen Powers of the Picket Fence by Pavement. The chorus consists of "R.E.M!" and SM opens the song by saying something along the lines of "There's a lot of bands i've name dropped, but one we haven't done yet is R.E.M." whole song is about REM.

Noah23 - Chicken Pox (23 Skidoo)
Every song by the Game mentions Dr. Dre
Dr. Dre - Let Me Ride (Aerosmith)

Also very good ones. Can't believe I forgot the CSS one.

Neil Young - From Hank to Hendrix