Of course the "award of merit" goes to the "author" for the composition in any case, but occasionally you may have some covers which are better than the original song (at least subjectively).
I have two, for my taste, to mention as my favorites:

This is a fantastic song of PJ!! And great Lyrics, by the way! But i really like more the Juliette version for the adding of the dash and vigor i was missing in the original, in a way...

And then this one, almost for the same reason:

This cover is excellent!! And so perfectly executed!!
Well done Glitter Dick! Devilish good job! <3

Looking forward to discover some more! Yours!

I met Eugene and Faye when they DESTROYED in what I firmly believe was their first Chicago appearance , ever (The singer in the opening band insisted they played at the legendary Tuts' to about 15 people , ca. 1978. I was'nt buying it.) , and they could'nt have been more pleasant. "Et was sooch a LARVELY crowd !" - Faye.
 
Tersicore said:

Good cover indeed!
The drums is so straight! remind me a german battle tank, a Panzer, somehow!;) 

Andy Climax said:

Better than the original? More punk definitely. Best of all.... She's Scottish, haha. Amazing stuff

MY FAVORITE VERSION OF THE OFT - COVERED BILL HALEY SONG, SKINNY MINNIE , IS BY THE SONICS. THEY SOUND, AS USUAL , LIKE THEY WERE OUT FOR BLOOD. SAM BUTERA DID A COOL VERSION , TOO.

I believe "SOAPY" was a Lyres original , but Fortune and Maltese bettered it as "Ken Bergland - Action Man" with new lyrics , and I topped neither of them , but , did it all the same , as "Doug Freedman - King of Men". Doug's in the Hideout. You should be honored to be his friend.

The Renegades , Fuzztones , and T.Tex Edwards all did cool versions of "13 Women".

I heard ecstatic field reports about The Hate Bomb's shows , but , I never saw them.

For Covers better than the originals, usually when the Hatebombs covered something it was better than the original...  

Soapy (the Lyres originally I think)

My brother the Man (We The People)

You Burn Me Up and Down (also We The People)

I've Been Thinkin' (Paul Bearer and the Hearsemen)

Stop It Baby (The Heard)

This list could go on and on...  unfortunately mostly you had to see them live as the few recordings they have don't really measure up to them live.

Of course anything the Mummies covered became theirs...  like Skinny Minny, it blows the Billy Hailey originally away...  although Gerry and the Pacemakers did a pretty cool version ....  really I just like to see this to see that awesome Croc Trixon Telstar that the drummer is playing..

http://youtu.be/J3Mihpptg3Y

But I think my favorite cover is the Renegades cover of 13 Women

http://youtu.be/wYsRpPImDS0

(original from Bill Haley http://youtu.be/HP7lIjlJ2I4)

I know this is late and all, but the original for "Come On Up" wasn't The Hugger Muggers it was The Rascals:

http://youtu.be/kliegM-1h_8

I like the Weirdos' original because of the more raw, less compressed production and INCREDIBLE ear-bending, stringbending out-of-tune guitarness, but they are both great. Love the cheesey organ in F.F.L's version. Thanks for posting both!
 
Dead Boy said:

The Weirdos' original "Life Of Crime" is killer!  But Flesh For Lulu's version is a little better than the original.

The Weirdos' original "Life Of Crime" is killer!  But Flesh For Lulu's version is a little better than the original.

you have me curious now! (i bet it does beat the original)

dave said:

Shit, Youtube deleted the Oblivions cover (it's on Popular Favorites)

Good cover indeed!
The drums is so straight! remind me a german battle tank, a Panzer, somehow!;) 

Andy Climax said:

Better than the original? More punk definitely. Best of all.... She's Scottish, haha. Amazing stuff

Not sure if this counts???

Better than the original? More punk definitely. Best of all.... She's Scottish, haha. Amazing stuff

Shit, Youtube deleted the Oblivions cover (it's on Popular Favorites)

Yep, a very dynamic and interesting cover!!. Didn´t know this guy! Love it!
This beat for sure the psychobilly version, (which doesn´t beat the original but is fun)!
:)

The Fnords said:

This is good too, very different from the original. D.

http://www.youtube.com/watch?v=IDiAP8JgD2s

Awesome cover!

Miss Strange said:

I've always dug Big Blacks cover of "the Model"

https://www.youtube.com/watch?v=D_tK1xw8AzA

over Kraftwerks original (funny how dated the intro sounds)

https://www.youtube.com/watch?v=OQIYEPe6DWY

I've always dug Big Blacks cover of "the Model"

https://www.youtube.com/watch?v=D_tK1xw8AzA

over Kraftwerks original (funny how dated the intro sounds)

https://www.youtube.com/watch?v=OQIYEPe6DWY

 I'm partial to T.Tex Edwards' version , partly because he was one of the first people to cover it , that I know of , and mainly because he did a great job , without relying too heavily on the original. Southern Culture on The Skids did a really good verson , too.  Wanda was'nt aware the song had  a "Cult" following until she started touring again , and people began requesting it. I like The remake with The Cramps , but , for me , you can't beat the original , it has everything . That's Roy Clark doing the proto - psychedelic "Eastern" guitar .

Hey! This Born Bad series are awesome!! Cheers

Dead Boy said:

When I found that video of Tav Falco, I didn't know (remember) who played the original, but I just thought that I've heard that tune by someone somewhere.  I didn't even know who is Wanda Jackson (except her name), but now I found why I've heard it, because I have "Born Bad" volume one!!!
 
Tersicore said:

@Dead Boy, would be the Tav Falco your favorite? :)

When I found that video of Tav Falco, I didn't know (remember) who played the original, but I just thought that I've heard that tune by someone somewhere.  I didn't even know who is Wanda Jackson (except her name), but now I found why I've heard it, because I have "Born Bad" volume one!!!
 
Tersicore said:

@Dead Boy, would be the Tav Falco your favorite? :)

This is good too, very different from the original. D.

http://www.youtube.com/watch?v=IDiAP8JgD2s

Another song which is been covered to death is "Funnel of Love". Such a killer song!!
Extremely hard to say which is the best version or best cover. 
The original? Maybe unbeatable!  Or the one with Lux and Ivy?
I love the one from The Fall as well!  So a great version!
God! There are so many fantastic covers!..  Any favorite out there?

@Dead Boy, would be the Tav Falco your favorite? :)

You right!
I admit i had to peep in youtube to hear at the original again, but no dubt, the UKJ cover is just great!. 

Korsy said:

When it comes to covers, this will always remain one of my favorites.

Yeah, probably i´ve just mix up the title..

My memory is loused up, sometime.
For decades i´ve been thinking i´ve seen Nirvana only once in Chicago ´91 and just recently i discovered that they came to play ´89 in the place i was working in Berlin and on top of that, we were sleeping in the same flat and having party together.. just gone! :(

John Battles said:

i COULD SEE THE CRAMPS DOING "JUNGLE"....We are all faltering , somehow , in our musical memories. I'm sure I saw some great bands , some that became well - known , but , beats me who they were.
 
Tersicore said:

Upppssss!!!
Why i thought the Cramps did cover this song?? Shit!, no idea!   (Ok..maybe just smoked too much back then...or getting old lately?). They didn´t!  ;D  but Gun Club did, for sure!!! In Miami, and how!!!  

Yeah, 8 eyed spy were special!! but missed Rudi and Lydia together, somehow....


John Battles said:

THAT WAS KIND OF A JOKE , BECAUSE "STRAY CAT STRUT" DOES SOUND LIKE IT WAS LIFTED DIRECTLY FROM " BLANK GENERATION". DID GUN CLUB DO "RUN THROUGH THE JUNGLE " , TOO? I'VE NEVER HEARD OF THE CRAMPS DOING IT.....LUX WAS A BIG CCR FAN  , THOUGH. EIGHT EYED SPY (W/LYDIA LUNCH) DID SOME COOL COVERS , LIKE "LIGHTNING'S GIRL" (NANCY SINATRA) , MAINTAINING MY COOL (SONICS) , DIDDY WAH DIDDY (CAPT. BEEFHEART'S VERSION.) , TOO. YOU KNOW , RUDI BRIEFLY PLAYED IN A MORE BLUESEY BAND CALLED THE DEVIL DOGS WITH LYDIA.  I THINK THEY ONLY DID A EUROPEAN TOUR. I'VE NEVER HEARD OF ANY RECORDINGS TURNING UP.

When it comes to covers, this will always remain one of my favorites.

I care because I can get 12-15 bucks each for their lps! That's my extent.

John Battles said:

I'm decades past caring about The Violent Femmes , but , this has GOT to be the better of the two , tho' he sounds like he's taking it seriously.....
 
Glenn Barton said:

I like the cover better for sure on this one.

Dead Boy said:

Violent Femmes - Do You Really Want To Hurt Me

I haven't heard the whole of the original, but I'm pretty sure this cover beats it.