The Collaborative International Dictionary of English v.0.48:

Beg \Beg\, v. t. [imp. & p. p. Begged; p. pr. & vb. n.
   Begging.] [OE. beggen, perh. fr. AS. bedecian (akin to
   Goth. bedagwa beggar), biddan to ask. (Cf. Bid, v. t.); or
   cf. beghard, beguin.]
   1. To ask earnestly for; to entreat or supplicate for; to
      beseech.
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            I do beg your good will in this case. --Shak.
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            [Joseph] begged the body of Jesus.    --Matt. xxvii.
                                                  58.
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   Note: Sometimes implying deferential and respectful, rather
         than earnest, asking; as, I beg your pardon; I beg
         leave to disagree with you.
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   2. To ask for as a charity, esp. to ask for habitually or
      from house to house.
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            Yet have I not seen the righteous forsaken, nor his
            seed begging bread.                   --Ps. xxxvii.
                                                  25.
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   3. To make petition to; to entreat; as, to beg a person to
      grant a favor.
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   4. To take for granted; to assume without proof.
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   5. (Old Law) To ask to be appointed guardiln for, or to aso
      to havo a guardian appointed for.
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            Else some will beg thee, in the court of wards.
                                                  --Harrington.
      [1913 Webster] Hence:

   To beg (one) for a fool, to take him for a fool.
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   I beg to, is an elliptical expression for I beg leave to;
      as, I beg to inform you.

   To beg the question, to assume that which was to be proved
      in a discussion, instead of adducing the proof or
      sustaining the point by argument.

   To go a-begging, a figurative phrase to express the absence
      of demand for something which elsewhere brings a price;
      as, grapes are so plentiful there that they go a-begging.
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   Syn: To Beg, Ask, Request.

   Usage: To ask (not in the sense of inquiring) is the generic
          term which embraces all these words. To request is
          only a polite mode of asking. To beg, in its original
          sense, was to ask with earnestness, and implied
          submission, or at least deference. At present,
          however, in polite life, beg has dropped its original
          meaning, and has taken the place of both ask and
          request, on the ground of its expressing more of
          deference and respect. Thus, we beg a person's
          acceptance of a present; we beg him to favor us with
          his company; a tradesman begs to announce the arrival
          of new goods, etc. Crabb remarks that, according to
          present usage, "we can never talk of asking a person's
          acceptance of a thing, or of asking him to do us a
          favor." This can be more truly said of usage in
          England than in America.
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WordNet (r) 3.0 (2006):

begging
    n 1: a solicitation for money or food (especially in the street
         by an apparently penniless person) [syn: beggary,
         begging, mendicancy]

Moby Thesaurus II by Grady Ward, 1.0:

23 Moby Thesaurus words for "begging":
   adjuratory, appealing, beggary, beseeching, bumming, cadging,
   entreating, imploring, mendicancy, mendicant, mendicity, mooching,
   panhandling, petitionary, pleading, prayerful, precative,
   precatory, scrounging, suppliant, supplicant, supplicating,
   supplicatory