Do unused parachutes need to be repacked? If so how often and why?
Yes, parachutes need to be repacked regularly. The length of the interval depends on the material of the parachute and is between 60 and 180 days. Every parachute should have a small pocket with a piece of paper which lists the most recent repack date and the name of the packer (who needs to comply with FAR part 65, subpart F).

FAA part 91.307 says:


  (a) No pilot of a civil aircraft may allow a parachute that is
  available for emergency use to be carried in that aircraft unless it
  is an approved type and has been packed by a certificated and
  appropriately rated parachute rigger—
  
  (1) Within the preceding 180 days, if its canopy, shrouds, and harness
  are composed exclusively of nylon, rayon, or other similar synthetic
  fiber or materials that are substantially resistant to damage from
  mold, mildew, or other fungi and other rotting agents propagated in a
  moist environment; or
  
  (2) Within the preceding 60 days, if any part of the parachute is
  composed of silk, pongee, or other natural fiber or materials not
  specified in paragraph (a)(1) of this section.


The reason should be clear from the regulation: If moisture is present, the growth of mold may prevent the parachute from unfolding easily.

For the T-10D parachute, which is the standard US Army parachute for airborne assault operations, the repack period is 120 days.