Why do artists cover other people's music?

I feel that artists cover other people's music because they believe that this will gain them the same success as the original song did. There have been successful cover songs over the years, with the most recent the release of the X Factor winner Alexandra Burke's version of "Hallelujah". This song was originally sang by Leonard Cohen, however has also had successful covers by Jeff Buckley, Rufus Wainwright and Allison Crowe. This was a huge success for Alexandra Burke, making her single the fastest-selling single by a female solo artist (although this was probably fuelled further by the hype of the X Factor!). Despite this, artists will often get critised for not using their own material but is this really a worry to them when recording a cover song brings them money, fame and success?!