A song murdered by someone.

Any version of "Unchained Melody" outside of the Platters.
Lauren Hill with her idiotic warbling of "Killing Me Softly".
Any remake of "What You Won't Do For Love" by Bobby Caldwell.

I love the Concrete Blonde "Everybody Knows."   I have it on the soundtrack album for "Pump Up the Volume."  There are LOTS of terrific covers of Leonard Cohen songs.  Mostly because the songs are well written, but it is also probably the case that his performance will not fit everyone's taste, so his version does crowd out contenders.

I particularly like an R.E.M. cover of "First We Take Manhattan."  

I hate to say this, but what about "Dancing in the Street" by David Bowie and Mick Jagger (an MTV Award winning video, if I recall.)

I believe Family Guy played the entire video on an episode as a joke. Oddly, I never heard it (or paid attention to it.)

I think I blacked out for a portion of time while watching it...

A great song is open to a lot of different interpretations/versions.  I think "Unchained Melody" is a great song.  There are more than 1500 recorded versions of that song, and MANY are worthy of being played even if the Righteous Bros. version is generally regarded as the standard bearer.  I have a number of the Righteous Bros. albums, including original release vinyl, but, that does not mean I don't like other versions of their biggest hit.  For example, I frequently listen to this version from 1960:

https://www.youtube.com/watch?v=fV8XwoIGo5M

Anybody who tries to cover House of the Rising Sun.  Very hard to beat Eric Burden and the Animals version.  And, they were one of the first groups to have a top ten record, that played longer than 2 1/2 minutes on the radio format.