I kinda like Guns and Roses covers, such as "Live and Let Die" and "knockin on Heaven's Door."
There are some people whose voice I like a lot, but, when they cover favorite songs, it almost hurts to hear the travesty. The ultimate one woman wrecking crew for me is Linda Ronstadt:
"Alison" (Elvis Costello)
"Carmelita" and "Hasten Down the Wind" (and a whole bunch of other Zevon songs)
"Blue Bayou" (Orbison)