Best Covers

I nominate J. Cash's cover of "The Mercy Seat" a cover of Nick Cave And The Bad Seeds from the 1988 release Tender Prey. On the lighter side, Any cover that I've heard by Big Head Todd And The Monsters, or Lake Street Dive has been excellent (both BHTATM, and Lake Street Dive get mucho play at my house, most of the catalog is on CD)...

my little garage punk band did Leonard Cohen's "Teachers" my favorite, since I got to croak it.

Hauser And Girlfriend Benedetta Caretta Perform Awesome Cover Songs - The Music Man

In addition, for those who like the Disturbed cover of Sounds of Silence, they did it live on Conan and a Google search will find it. Even better than the official version posted above. 

Also, for the wildest covers out there, anything by 2cellos. Lots of stuff to find on the net.

Cheers,         Crazy Bill

Leonard Cohen covers have been mentioned throughout.

Great CD of covers: I'm Your Fan

The songs of Leonard Cohen by:

R.E.M., Ian McCulloch, Pixies, and many others