The Collaborative International Dictionary of English v.0.48:

Crave \Crave\ (kr[=a]v), v. t. [imp. & p. p. Craved
   (kr[=a]vd); p pr. & vb. n. Craving.] [AS. crafian; akin to
   Icel. krefja, Sw. kr[aum]fva, Dan. kr[ae]ve.]
   1. To ask with earnestness or importunity; to ask with
      submission or humility; to beg; to entreat; to beseech; to
      implore.
      [1913 Webster]

            I crave your honor's pardon.          --Shak.
      [1913 Webster]

            Joseph . . . went in boldly unto Pilate, and craved
            the body of Jesus.                    --Mark xv. 43.
      [1913 Webster]

   2. To call for, as a gratification; to long for; hence, to
      require or demand; as, the stomach craves food.
      [1913 Webster]

            His path is one that eminently craves weary walking.
                                                  --Edmund
                                                  Gurney.

   Syn: To ask; seek; beg; beseech; implore; entreat; solicit;
        request; supplicate; adjure.
        [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Crave \Crave\, v. i.
   To desire strongly; to feel an insatiable longing; as, a
   craving appetite.
   [1913 Webster]

         Once one may crave for love.             --Suckling.
   [1913 Webster]

WordNet (r) 3.0 (2006):

crave
    v 1: have a craving, appetite, or great desire for [syn:
         crave, hunger, thirst, starve, lust]
    2: plead or ask for earnestly

Moby Thesaurus II by Grady Ward, 1.0:

70 Moby Thesaurus words for "crave":
   ache, adjure, appeal, appeal to, apply for, ask, ask for,
   aspire after, beg, beg leave, beseech, bespeak, brace, call for,
   call for help, call on, call upon, choose, clamor for, conjure,
   covet, crave after, crawl after, cry for, cry on, cry to, demand,
   desiderate, desire, dream, entreat, file for, hanker, hanker after,
   hunger, hunger after, impetrate, implore, importune, imprecate,
   indent, invoke, kneel to, lust, lust after, make a request,
   make a requisition, make application, necessitate, obtest, order,
   pant after, pine, plead, plead for, pray, put in for, request,
   require, requisition, run mad after, run to, sigh, supplicate,
   take, thirst, thirst after, want, whistle for, wish