Torm said:
"Knockin' On Heaven's Door" by Avril Lavigne, originally by Bob Dylan
"Knockin' On Heaven's Door" by Guns and Roses, originally by Bob Dylan
You say you like both of these? Different tastes, I guess - it's quite possible I like the second better than the original, but I find Avril's version quite painful to hear. :/
Torm said:
"Come On Eileen" By Save Ferris, originally by Dexy's Midnight Runners
Original was a great song, useful as a 'trump song' for driving other annoying tunes out of your head. I have an a cappella group called Rockapella covering it. Good stuff. Little known fact: Dexy's Midnight Runners also had other songs. Crazy!
Some other good covers:
Nightwish doing Ozzie's "Crazy Train" live. I can't for the life of me find a decent quality rip, though.
Mike Oldfield doing Gershwin's "I Got Rhythm"

Queensryche doing Kansas's "Dust in the Wind". Sarah Brightman also does a decent cover of that one. She also does a decent cover of Queen's "Who Wants to Live Forever".
What I really like, though, is rock bands doing old folk songs. Observe -
Nightwish - Over The Hills And Far Away
Mudmen - Drink And Fight
Buck O' Nine - Irish Drinking Song
Metallica - Whiskey In The Jar
Also, while not really rock, Mike Oldfield's "Women of Ireland" and Sarah Brightman's "So Many Things" both take from the same original folk song.
Trans-Siberian Orchestra has some great takes on some old Christmas tunes, and (on a different album) some of Beethoven's works.
I suppose the two drinking songs aren't strictly covers, but whatever. Also, if all you metal fans want to hear the original of Whiskey In The Jar, look up The Pogues.
Oh, and pretty much everything on Rush's "Feedback" album is cool.
Finally, if you enjoy this kind of thing, I suggest spending some time alone with your P2P app of choice and the
Covers Project.
--Impeesa--