Welcome to Smogon! Take a moment to read the Introduction to Smogon for a run-down on everything Smogon, and make sure you take some time to read the global rules.
pomplamoose does a lot of great, kinda quirky covers like this one: my favorite things
i am a sucker for nataly dawn's voice and also her face maybe welp
also madeleine peyroux (another lovely voice) has a pretty sexy rendition of dance me to the end of love, probably the only leonard cohen cover i've enjoyed more than the original
You really need to check out all of 99 Songs of Revolution Vol. 1 by Streetlight. All amazing covers except for, ironically, when they cover their own song.
Vader - Fight Fire with Fire (Metallica Cover)
Vader is a great death metal band, and they really made a thrash song sound more like death metal, which is pretty cool, considering this is one of my favorite metallica songs.
I love pretty much all of the songs Judas Priest have covered. There's just something about turning an old Joan Baez folk song into something else that sounds cool. :)
I never was a fan of Garage Inc. I prefer Thin Lizzy's take on the traditional Irish song and Thin Lizzy in general over Metallica. The $5.98 E.P.: Garage Days Re-Revisited in my opinion are Metallica's best covers.