I think Shinedown's cover of Lynyrd Skynyrd's Simple Man is better than the original. They put more feeling into the song IMO.

YouTube - Shinedown - Simple Man

Since I don't like Lynyrd Sknyrd I'm inclined to agree.

My favourite covers are:

Jimi Hendrix - All Along The Watchtower (Bob Dylan)
The Violent Femmes - Children Of The Revolution (T.Rex)
The Byrds - My Back Pages (Bob Dylan)
The White Stripes - Jolene (Dolly Parton)
The Byrds - Mr. Tambourine Man (Bob Dylan)
Ani DiFranco - Wishin' And Hopin' (Dusty Springfield)

Bob Dylan was an okay songwriter.

The two big, well-known ones that always come to mind for me are:

• Devo's cover of the Rolling Stones' "Satisfaction"
• Cowboy Junkies' cover of the Velvet Underground's "Sweet Jane"

But all these are also great:

• Alien Sex Fiend's cover of the Cramps' "Silver Machine"
• Cornelius's cover of the old, old song "Brazil" (according to Wikipedia written by someone named Ary Barroso)
• Faith No More's cover of the Dead Kennedys "Let's Lynch the Landlord"
• The super-sleezy Motorhead/Wendy O. Williams cover of Tammy Wynette's "Stand By Your Man"
• Mike Ness' cover of Bob Dylan's "Don't Think Twice"
• REM's cover of the Velvet Underground's "Pale Blue Eyes"
• Also REM's cover of the Clique's "I Am Superman"

FNM had some great covers. Their "War Pigs" is better than the original by a highway mile. Good call.

I don't know if its because I have a huge bias in favor of both Black Sabbath and Dead Kennedys but I find both of those covers to be insulting when compared to their source material.

KMFDM's cover of Material Girl is probably the best cover ever.

I really like U2's live cover of "Helter Skelter" on Rattle & Hum.

Oh, and also, Travis' cover of Britney's "Baby One More Time" is delightful as well. As is Franz's live cover of Gwen Stefani's "What You Waiting For?".

i think Queens Of The Stone Age did a rather nice cover of Elliot Smith's Christian Brothers.

im going to say..
Crazy-Mushroomhead seal cover.
*** on feel the noize-Quiet Riot slade cover.