I can think of several. Off the top of my head and in no particular order:
"Macarthur Park" (The Negro Problem)
"Come as You Are" (Caetano Veloso)
"Friend of the Devil" (Lyle Lovett)
"Everybody's Happy Nowadays" (Carter the Unstoppable Sex Machine)
"Oops I Did It Again" (Richard Thompson)
"Supernaut" (Black Box version, 1,000 Homo DJs w/Trent Reznor)
"Tiempo Sin Respuesta" (Pedro Aznar, cover of Nick Drake's "Time of No Reply")
And I'll second (or third, or whatever) the Johnny Cash version of "Hurt."