Just on the top of my mind...

Northern Kings (a Nightwish 'spin-off') have a quite different version of Wanted.
A Black Metal band called Catamenia have a version of Born to Be My Baby
There is a live cover of Wanted done by this All Star band with Dave Navarro, Matt Sorum and Corey Taylor (edit: Camp Freddy is the name of the project)

Corey Taylor himself covered Wanted and Prayer several times actually
Melissa Etherdige covered Wanted several times
Opeth have covered Wanted (some may say it's a bit of a spoof though which I don't think it is)
Dream Theater have done a cover but I've only heard snippets of it
People like Nickelback or Daughtry have done covers of Wanted.

Edguy have covered Runaway
Edit: The Edguy one...so much fun, even if the chords are all messed up

A lof of smaller Black Metal bands have covered Runaway actually....Walhalla and Blind Stare are two that come to my mind. I guess the song lends itself quite naturally to black metal

Edit 2: Oh yes....I've seen the Gorillaz do some wicked cover of Bad Name in their live shows. Was lots of fun!

There's a lot more covers of Wanted by all kinds of people really...just proves that if there was one song only, it'd be the mighty Wanted Dead Or Alive.