Three immediately leap to mind:

Pet Shop Boys' stunning version of Always On My Mind (a number one smash in the UK during Christmas/New Year 1987/8).

U2's splendid cover of Unchained Melody (on the B-side of their 1989 single All I Want Is You).

Gary Jules lovely alternative take on Mad World (another Christmas number one hit in the UK, this time in 2003).

All of the above examples exemplify the most important thing with a cover version, ie to make it your own, don't just perform karaoke.