I was trying to think of a Depeche Mode cover that improved the Depeche version. There aren't any. Gravity Kills do a decent
Personal Jesus, Rammstein do a cool
Stripped, Deftones do a meaty
To Have and to Hold and In Flames heavily brutalise
Everything Counts, but no one beats the Mode it seems.
Marilyn Manson and Lacuna Coil, of course, ruined their songs.