My favourite band Ghost, a Swedish rock/metal group, have a history of doing covers which you wouldn't expect them to do, song which don't fit into their usual genre.
Their whole gimmick is that they're a satanic parody of the Catholic Church so all of their covers are songs with names that could also have satanic/anti-religious themes.
I've you've never listened to them I urge you to give them a go, they are not what you imagine ands their music is often upbeat, poppy and melodic.
Here are some of my favourite covers done by them:
Here Comes the Sun (Beatles)
If you have Ghost (Roky Erickson)
It's a Sin (Pet Shop Boys)
Missionary Man (Eurythmics)
I'm a Marionette (ABBA)