Based on a discussion with Adam (He's got his own, secret, list that i'm sure he's put more thought into than me), here's my list of the best cover songs.

The rules:

1. The song has to be good. (!)
   
2. The song shouldn't be a straight ("faithful") cover of the original - might as well listen to the original.
   
3. However, the song has to still retain the spirit of the original, meaning it can't just be a whole new song with the same lyrics.
   
4. It should highlight some aspect about the original song, or make you look at the original in a new way.
   
5. It should highlight an aspect of the band that is covering it, showing how the band has developed from their influence and contributed something new to music.
   
6. The covering band can't contain any members of the original band. So you can't count, for example, some fantastic Ozzy version of a Black Sabbath song with Randy Rhodes on guitar. For these purposes, a producer is considered a member of the band. So John Cale's cover of the Modern Lover's Pablo Picasso can't be counted.
   

The top five:

1. The Slit's cover of Marvin Gaye's Heard It Through The Grapevine
   
2. The Cure's cover of Jimi Hendrix's Purple Haze
   
3. Disposable Heroes of Hiphophrosy's cover of the Dead Kennedy's California Uber Alles
   
4. Johnny Cash's cover of U2's One
   
5. Anti-Nowhere League's cover of the traditional Streets of London
   

Honorable Mentions:

1. John Cale's cover of Elvis Presley's Heartbreak Hotel (a little too much in violation of rule #3
   
2. Metallica's cover of Holocaust's The Small Hours (nearly breaks rule #2)
   
3. Jimi Hendrix's cover of Bob Dylan's All Along The Watchtower
   
4. White Zombie's cover of Black Sabbath's Children of the Grave
   

I purposely excluded covers of blues songs. Adding all the reinterpretations of blues songs by Jimi Hendrix, Cream, Led Zeppelin, and others was just too monstrous of a task. What this means is that i had to exclude the holy trinity of Big Joe William's Baby Please Don't Go covers by Them, AC/DC, and Budgie. This made me very sad.

Similarly, i excluded covers of classical music, so i didn't consider Emerson Lake and Palmer interpretations of things like The Barbarian and Pictures at an Exhibition.

Lastly, i didn't include covers of the Velvet Underground's All Tomorrow's Parties, since that's its own list.

i was only witholding my list because a) i was making sure i was giving it the proper thought and b) i was writing up individual explanations for each song. i dont know what im gonna do with those explanations now, maybe publish them in a separate place.

covers are tricky business, you have to be faithful and deviant at the same time. the rules here are good guidelines, but i dont endorse them as a) complete or b) necessarily mandatory. anyway, here is my list with very little overlap from rod's:

(in loose order with a tie for 5th place)

All Along the Watchtower - Jimi Hendrix (Bob Dylan)
Lola - The Raincoats (The Kinks)
Microphone Fiend - Rage Against the Machine (EPMD)
Black Steel - Tricky (Public Enemy)
Burning Up - Babyland (Madonna)
Waiting for the Man - Sheep on Drugs (The Velvet Underground)

honorable mention:

Dissident Aggressor - Slayer (Judas Priest)
Helter Skelter - Siouxsie and the Banshees (The Beatles)

Helter Skelter - Siouxsie and the Banshees (The Beatles) - Charles Manson stole that song from the Beatles, and then Aerosmith stole that song from Charles Manson, and then Motley Crue stole that song from Aerosmith, and then U2 stole it "back".

all good choices, btw.

i'm surprised and relieved to see Rammstein's cover of Stripped by Depeche Mode was not part of anyone's list.

not in any order, but top 5 nonetheless:

war pigs - the dresden dolls (black sabbath)
penny royal tea - kristin hersh (nirvana)
the amorous humphrey plugg - chris connelly (scott walker)
the jeweller - this mortal coil (pearls before swine)
barracuda - rasputina (heart)

honorable mentions:
superstar - sonic youth (the carpenters)
dear prudence - siouxsie and the banshees (the beatles)
everybody's got something to hide (except for me and my monkey) - kristin hersh (the beatles)
all 5000 covers of all tomorrow's parties I have
the mark kozelek AC/DC cover album I love that you hate
i could go on but I'll stop!

i actually have kozelek's 'what's next to the moon' (the song) on my iPod.

I have to hear the dresden doll's war pigs and rasputina's barracuda; they *have* to be good.

i don't like the jeweller, but i never heard the original. I almost gave Late Night an honorable mention, but the list was getting too long.

The Dresden Dolls have only done war pigs live, but it's awesome. There's a bunch of live copies of it at http://www.automaticjoy.com/

I think we might even have some video of them doing it when we saw them in Portland.

The Rasputina version of Barracuda is on their live cd, A Radical Recital. One of (if not) the greatest live recordings ever.

And yeah, you can pick just about any This Mortal Coil song, but I think the Jeweller is my favorite.