Best covers

Eva Cassidy - Fields Of Gold
Eva Cassidy - Time After Time

frou frou-holding out for a hero

Indigo Girls - Tangled Up in Blue

Marilyn Manson-Sweet Dreams
Marilyn Manson - Tainted Love

Ani DiFranco with Maceo Parker- When You Were Mine (Prince)


Foo Fighters - Down in the park

The Manson cover of Down in the park was killer too.
 
Foo Fighters - Darling Nikki (Prince)
The Bangles - California Dreamin' (The Mamas and The Papas)
The Sundays - Wild Horses (Rolling Stones)
 
there are a bunch of albums called the BYO Split Series where they take two punk bands and they cover a few of each others songs. There are some great covers on these.

Vol 1. Leatherface and Hot Water Music
Vol 2. Swingin' Utters and Youth Brigade
Vol 3. Nofx and Rancid
Vol 4. Anti-Flag and Bouncing Souls
Vol 5. Alkaline Trio and One Man Army
 
Good Riddance - Come Dancing (The Kinks)
Lagwagon - Brown Eyed Girl (Van Morrison)
Propagandhi - I Want you to Want Me
Slayer - Filler/I Don't Want to Hear It (Minor Threat)
RHCP - Higher Ground (Stevie Wonder)
Tool - No Quarter (Led Zeppelin)
NOFX - Last Caress (Misfits)
 
Lacuna Coil - Enjoy the Silence (depeche mode)
Mushroomhead - Crazy (Seal, I think)
Fear Factory - I Will Follow (U2)
Fear Factory - Millennium (Killing Joke, I think)
In This Moment - Broken (Pantera) pretty damn good cover IMO
[ame="http://www.youtube.com/watch?v=-hB4n5wg7b4"]YouTube - In This Moment Jam on Talking Metal[/ame]

For that matter, any cover song Fear Factory has done is awesome. Every album they've done just about has one cover song, at least.