The Collaborative International Dictionary of English v.0.48:

Shopper \Shop"per\, n.
   One who shops.
   [1913 Webster]

WordNet (r) 3.0 (2006):

shopper
    n 1: someone who visits stores in search of articles to buy
    2: a commercial agent who shops at the competitor's store in
       order to compare their prices and merchandise with those of
       the store that employs her