The Collaborative International Dictionary of English v.0.48:

Accomplish \Ac*com"plish\, v. t. [imp. & p. p. Accomplished,
   p. pr. & vb. n. Accomplishing.] [OE. acomplissen, OF.
   accomplir, F. accomplir; L. ad + complere to fill up,
   complete. See Complete, Finish.]
   1. To complete, as time or distance.
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            That He would accomplish seventy years in the
            desolations of Jerusalem.             --Dan. ix. 2.
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            He had accomplished half a league or more.
                                                  --Prescott.
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   2. To bring to an issue of full success; to effect; to
      perform; to execute fully; to fulfill; as, to accomplish a
      design, an object, a promise.
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            This that is written must yet be accomplished in me.
                                                  --Luke xxii.
                                                  37.
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   3. To equip or furnish thoroughly; hence, to complete in
      acquirements; to render accomplished; to polish.
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            The armorers accomplishing the knights. --Shak.
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            It [the moon] is fully accomplished for all those
            ends to which Providence did appoint it. --Wilkins.
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            These qualities . . . go to accomplish a perfect
            woman.                                --Cowden
                                                  Clarke.
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   4. To gain; to obtain. [Obs.] --Shak.
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   Syn: To do; perform; fulfill; realize; effect; effectuate;
        complete; consummate; execute; achieve; perfect; equip;
        furnish.

   Usage: To Accomplish, Effect, Execute, Achieve,
          Perform. These words agree in the general idea of
          carrying out to some end proposed. To accomplish (to
          fill up to the measure of the intention) generally
          implies perseverance and skill; as, to accomplish a
          plan proposed by one's self, an object, a design, an
          undertaking. "Thou shalt accomplish my desire." --1
          Kings v. 9.
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                He . . . expressed his desire to see a union
                accomplished between England and Scotland.
                                                  --Macaulay.
          [1913 Webster] To effect (to work out) is much like
          accomplish. It usually implies some degree of
          difficulty contended with; as, he effected or
          accomplished what he intended, his purpose, but
          little. "What he decreed, he effected." --Milton.
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                To work in close design by fraud or guile
                What force effected not.          --Milton.
          [1913 Webster] To execute (to follow out to the end,
          to carry out, or into effect) implies a set mode of
          operation; as, to execute the laws or the orders of
          another; to execute a work, a purpose, design, plan,
          project. To perform is much like to do, though less
          generally applied. It conveys a notion of protracted
          and methodical effort; as, to perform a mission, a
          part, a task, a work. "Thou canst best perform that
          office." --Milton.
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                The Saints, like stars, around his seat
                Perform their courses still.      --Keble.
          [1913 Webster] To achieve (to come to the end or
          arrive at one's purpose) usually implies some
          enterprise or undertaking of importance, difficulty,
          and excellence.
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WordNet (r) 3.0 (2006):

accomplish
    v 1: put in effect; "carry out a task"; "execute the decision of
         the people"; "He actioned the operation" [syn: carry
         through, accomplish, execute, carry out, action,
         fulfill, fulfil]
    2: to gain with effort; "she achieved her goal despite setbacks"
       [syn: achieve, accomplish, attain, reach]

Moby Thesaurus II by Grady Ward, 1.0:

122 Moby Thesaurus words for "accomplish":
   achieve, act, approach, arrive, arrive at, arrive in, attain,
   attain to, be productive, be received, blow in, bob up,
   bring about, bring into being, bring off, bring through,
   bring to completion, bring to fruition, bring to pass, carry off,
   carry out, carry through, cause, check in, clock in, come, come in,
   come to, come to hand, commit, compass, complete, conclude,
   conduct, consummate, cope with, crown with success, cut, deal with,
   discharge, dispatch, dispose of, do, do the job, do the trick,
   do to, effect, effectuate, eke out, enact, end, engineer, execute,
   fetch, fetch up at, fill in, fill out, find, finish, fulfill, gain,
   get by, get in, get there, get to, go and do, hack, handle, hit,
   hit town, industrialize, inflict, knock off, make, make good,
   make it, make up, manage, mass-produce, mature, overproduce, pay,
   perform, perpetrate, piece out, polish off, pop up, produce,
   pull in, pull off, punch in, put across, put away, put over,
   put through, reach, realize, refill, render, replenish, ring in,
   roll in, round out, score, show up, sign in, succeed, swing,
   take and do, take care of, time in, top off, transact,
   turn the trick, turn up, up and do, volume-produce, win, wind up,
   work, work out, wreak