I haven't heard anything off the second Nativity in Black, but the first one had some standout performances. I was introduced to what would become one of my favorite bands, Corrosion of Conformity on it. They didn't stray too far from the original, considering they haven't really strayed from Black Sabbath's sound at all in the last decade....
In terms of great covers, I'm surprised no one's given credit to Guns N' Roses for Mama Kin.
Red Hot Chili Pepper's cover of High Ground seems like an odd oversight for this forum as well.
I really love the Rollins Band cover of Ghost Rider by Suicide, but that might be too obscure, so might Degenerated as covered by DGeneration originally by Reagan Youth.
Soundgarden has done a few good covers, including Girl You Want by Devo.
Guns N' Roses Spaghetti Incident has some standout moments that certainly surpass the original, such as their Fear cover "I Don't Care About You." Slayer's cover album also boasts a couple standout tracks, but the originals are probably too obscure to be considered in this thread.
I also have to go on record as saying I disagree with the CCR version of Grapevine being an improvement. I am a huge CCR fan, but their version wanders around aimlessly. The band is great when knocking out rootsy southern blues tinged pop songs, but as a jam band they always seemed lacking.