Speaking of Public Enemy, I like the remake of their own song they did w/ Anthrax better than their original, though both are really cool songs IMO.
As for MJ songs, I like Alien Ant Farm's Smooth Criminal a lot, and David Ruffin's I Want You back a lot (though not more than the originals, though I'm biased lol, so I'll give 'honorable mention').
Jimi Hendrix's cover of All Along the Watch Tower (Dylan original).
Hendrix's cover of Like a Rolling Stone from the '67 Monteray Pop Festival (Dylan orignal).
Rolling Stones' Just My Imagination (Temptations, though I may like the original better, but the cover is damn good IMO).
Stevie Wonder's "We Can Work It Out" over the Beatles, though I like the Beatles too.
Stevie Wonder's "Blowing in the Wind" (Dylan original)
Jermaine Jackson's/Jackson 5's "Bridge over Troubled Water" (Simon & Garfunkle)
Otis Redding's Satsifaction (Rolling Stones)
Jackson 5's "Who's Loving You" (Smokey Robinson and the Miracles)
Guns N Roses' Live and Let Die (Paul McCartney)
Guns N' Roses' Knockin on Heavin's Door (album cut; Dylan)
There's lots of good covers out there, but just using as criteria as preferring one over the other, I think that's all I could think of for now.