The Collaborative International Dictionary of English v.0.48:

Beshrew \Be*shrew"\, v. t.
   To curse; to execrate.
   [1913 Webster]

         Beshrew me, but I love her heartily.     --Shak.
   [1913 Webster]

   Note: Often a very mild form of imprecation; sometimes so far
         from implying a curse, as to be uttered coaxingly, nay
         even with some tenderness. --Schmidt.
         [1913 Webster]

WordNet (r) 3.0 (2006):

beshrew
    v 1: wish harm upon; invoke evil upon; "The bad witch cursed the
         child" [syn: curse, beshrew, damn, bedamn,
         anathemize, anathemise, imprecate, maledict] [ant:
         bless]