Your vote for greatest (covers) album

Try Eva Cassidy "The Best of Eva Cassidy" 2 record set of all or almost all covered songs is the best for me. Her voice is angelic and spot on pitch wise.... almost chilling. Just beautiful. Hopefully you won't be disappointed.

second Rosanne’s The List....you inspired me to start my morning with her :)

Its a mix of originals and covers, but overall one of my favorite albums, Nirvana - MTV Unplugged

Ryan Adams - 1989

I love the man in black’s American series. Johnny’s cover of Hurt on American IV is pretty special

Abba-esque EP by Erasure really jumps first in my mind. Covering 4 ABBA songs and making it completely theirs. 

The Scissor Sisters glam, disco cover of Pink Floyd’s “Comfortably Numb” is so wrong...but yet so right

I don't know of any album sloppier than Sid Sings, but I, too, have enjoyed it a lot.
Yes, the Motorhead covers album is good, and I also liked Guns N' Roses' Spaghetti Incident and Metallica's Garage Days Revisited; both had a couple low points, but the highlights more than made up for it.In that same era, Slayer put out the note-worthy Undisputed Attitude, which had its moments and was mind-blowingly fast, even for Slayer.
My all-time favorite cover album, though, has to go to The Walkabouts' Satisfied Mind.  It is a phenomenal album by any measure.