More on this topic, since I like it so much (and so does Jim).

First, Michael Bowen says that Weird Al is a cover artist. I love Weird Al, and his music is great, but he's a parodist, not a coverist, at least in my book. It's okay to change a couple of words in a cover (mainly male artists changing "he" to "she" and vice versa, although it's often unnecessary), but to change all the lyrics makes a new song. Less obvious is the cover medley, such as recently seen done in the movie Moulin Rouge, which mixes several songs into a new one. Such a medley doesn't change the lyrics, but it often doesn't use the full set from each song.

But, to the topic at hand, my favorite covers, expanded from the previous post:

1. 1. "Train in Vain (Stand By Me)", originally by the Clash, as performed by Dwight Yoakam on Under the Covers. I used to hate country music, but I realized in these last few years that it's not the instruments or the sound, but the inane lyrics and poseurs with their fake accents that make up the contemporary scene. Yoakam's the real thing, and his accent is real, and by taking this song of betrayal and recasting it with fiddle, accordion and banjo works because it reveals the lyrics better than the Clash original (which I like, but I really never could hear those lyrics in their great beat).
2. "Rusty Cage," originally by Soundgarden, as performed by Johnny Cash on Unchained. First, it strips the music to an acoustic guitar with that great repeating bass figure. Then the chorus adds the other instruments. But it's hearing that voice sing "Too late to start a fire/I'm burning diesel, I'm burning dinosaur bones." The bridge, where the electric guitar kicks in, works so well with Cash's rugged voice, too. I have no idea what the original song is supposed to be about, and if I recall from the liner notes, neither did Johnny, but in his hands, it turns out to be one of his best songs about being a prisoner, and Cash is the master of those types of songs.
3. "Reason to Believe," originally by Bruce Springstein, from Michael Penn and Aimee Mann off the Badlands tribute album. I've never been a Springstein fan, although I did see him perform in 1985 during the "Born in the U.S.A." tour, and have to admit that he's a hell of a showman. But something about his voice has always bothered me (in the same way that Dylan's never appealed to me), and I've always liked it when others do his songs, from Patti Smith's "Because the Night" and Manfred Mann's "Blinded by the Light." So I never really heard Nebraska and have no song memory of the original, but that doesn't mean that I don't love this version by Penn and Mann, who do a simple duet over a acoustic guitar (the organ and drum background is almost inaudible for most of the song). Of course, I also like songs where both a man and a woman sing, so it has that going for it, as well.
4. "Atlantic City," originally by Bruce Springsteen, as performed by The Band on Jericho. There's a version of this song by Hank Williams III on the Badlands album, but that one shows how a country cover can go seriously wrong. The Band's version is as country as you get, but it works because Levon Helm is able to get into the narrator character's part, whereas Hank just sings the thing. The accordion helps a lot, too.
5. "Tomorrow Wendy," originally by Andy Prieboy, as performed by Concrete Blonde on Bloodletting.
   This is another song that I hadn't heard the original before I heard the cover. The live version of this really gets into some passionate outrage, which is partly why I like this song so much.
6. "Jack, You're Dead," originally by Louis Jordan, as performed by Joe Jackson on Jumpin' Jive. Jackson's Jumpin' Jive album was the record that turned me onto jazz swing, and especially the type as performed by Louis Jordan and Cab Calloway. Another great version of this song is done by B.B. King on his album of Jordan covers, Let the Good Times Roll. King's interjected comments (like, "My, my, don't he look natural") are better than Jackson's, but I like Jackson's sound.
7. "Kiss," originally by Prince, as performed by Tom Jones and the Art of Noise on Move Closer. I like the Prince version, but there's just something right about this song on womanizing sung by the welsh madman, and the electro-horn sound of Art of Noise really adds some punch to the song, including adding a little seque to their Dragnet re-do. "Think I better dance now..."
8. "Burning Down the House," originally by Talking Heads, as performed by Tom Jones and the Cardigans on Reload. This is an even stranger mixture, and yet...I think I like it as much as the original. Sometimes it's just how disparate the two voices are that makes a duet work, and that's how it works here: Jones' impassioned rough tenor versus Nina Persson's detached, smooth soprano. The lyrics don't make sense, on purpose, so the listener feeds into them whatever the performer makes of them, and in this case, as with almost anything Jones sings, it becomes all about sex. (While researching this, I ran across a reference to some Cardigan covers of Thin Lizzy's "The Boys are Back" and Ozzy Osbourne's "Mr Crowley." Oh, I'd love to hear those!)

That's all I can identify at the moment, although I'm sure there's many others, and more performed on stages around the world nightly.