Why does DES use exactly 16 rounds? Why does DES use exactly 16 rounds and not more or less than 16? What is the significance of using 16 rounds?
From Schneier's description of DES in Chapter 12 of Applied Cryptography (12.3): 


  DES with any number of rounds fewer than 16 could be broken with a known-plaintext attack more efficiently than by a brute-force attack.


This explains the "Why not less than 16".

As for the "why not more than 16", that is a tradeoff for speed of execution (more rounds = less speed).