I like Metal, so here's some covers geared toward that end of the musical spectrum:
The Absence - Into The Pit (Testament cover)
Anthrax - Keep on Runnin' (Journey cover)
Anthrax - Auf Wiedersehen (Cheap Trick cover)
Crowbar - Dream Weaver (Gary Wright cover)
Crowbar - No Quarter (Led Zeppelin cover)
Opeth - Would? (Alice in Chains cover)
Helloween - From Out of Nowhere (Faith No More cover)
Judas Priest - The Green Manalishi (Fleetwood Mac cover)
Mastodon - Emerald (Thin Lizzy cover)
Fu Manchu - Godzilla (Blue Oyster Cult cover)
Saxon - Ride Like The Wind (Christopher Cross cover, no, seriously, it's awesome)
Testament - Rapid Fire (Judas Priest cover)
Whitesnake - Basically all of their albums after Slide It In are covers of themselves!
Wolf - A Dangerous Meeting (Mercyful Fate cover)
Sleep - Snowblind (Black Sabbath cover)
All that said... my favorite cover of all time is Corrosion of Conformity's version of Black Sabbath's Lord of This World. They absolutely nail it. The drum and guitar sound is absolutely PERFECT; raw, gutteral, and just dirty enough to give it that sludgy stoner goodness the song deserves. It's one of the rare instances where the cover outshines the original, and the original is amazing in it's own right.