Why are both fuse and earthing are needed?
Fuses are typically to protect wiring and other components from overheating and perhaps catching fire and/or exploding in the event of a low-impedance fault.  From the Wikipedia article "Fuse (electrical)":


  A fuse interrupts an excessive current so that further damage by
  overheating or fire is prevented. Wiring regulations often define a
  maximum fuse current rating for particular circuits. Overcurrent
  protection devices are essential in electrical systems to limit
  threats to human life and property damage.


However, one could easily be electrocuted without tripping a breaker or blowing a fuse.  Thus, earthing a metal appliance, enclosure, plumbing, etc. prevents potentially lethal voltages from developing on these conductors.