Songs by bands that mention other bands in the lyrics or the title directly
 

Right now I can only think of:

Le Tigre - Hot Topic
LCD Soundsystem - Losing My Edge
Pavement - Range Life

Any others?

Bikini Kill - Thurston hearts the Who

Jimmy eat world - Authority song "The DJ never has it, JAMC Automatic."
Xiu Xiu - Ian Curtis wishlist

Only ones I could come up with right away.

Half Man Half Biscuit - Joy Division Oven Gloves

can't remember who it is but the song mentions listening to sufjan's michigan or illinoise, can't remember which either

yeah thats actually why i picked it as my user name back in 2005.

I think MIA namedrops the Pixies in a couple of her tracks.

The Wombats - Let's all dance to Joy Division

Awful, awful song.

Ciccone Youth - Two cool rock chicks listening to Neu!

Human League - The Things That Dreams are Made of

(Norman Wisdom, Johnny, Joey, Dee Dee, good times)

Xiu Xiu - Hives Hives(The Pogues)
Xiu Xiu - Ian Curtis Wishlist

The Replacements- Alex Chilton

sucidal tendencies mention suicidal tendencies alot

SY - Crème brûlée (Neil Young mentionned in the lyrics)
Neil Young - Borrowed tune (reference to the Rolling Stones, off course because the tune is directly borrowed from Lady Jane)
Badly Drawn Boy - You were right (references to Madonna, Sinatra, Buckley, Cobain & Lennon)

Cat Power - I Don't Blame You(Smog)

fish & sheep - keiji haino's haircut

Scissor Shock - Merzbow Tear Jerker
Scissor Shock - Johnny Merzbow's blah blah blah

sy - madonna, sean and me

Threre's so many...

sarram mentioned Pavement's "Range Life" and it made me think of their "The Unseen Power of the Picket Fence."

Sonic Youth - Screaming Skull

Okay, trying to think of these, I went waaay back...
Deep Purple - Smoke on the Water "Frank Zappa & the Mothers"

I don't know if you saw Conan with his "strike beard" haha playing his strat the other night. In the little video segment he was walking around with a guitar and an amp strapped to his back torturing NBC staffers with the riff from "Smoke on the Water."
A jam of Radiohead's "Creep" was fun, as was a hilarious version of Beastie Boys' "Sabotage" while singing it like Edith Bunker (Jean Stapleton from classic TV's "All in the Family"). During this brief shot of him playing down a hallway, an actually good-sounding snippet of one of my favorite songs to play, "Purple Haze," could be heard.

Sonic Youth - Hot Wire My Heart

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