The Collaborative International Dictionary of English v.0.48:

Appreciate \Ap*pre"ci*ate\, v. t. [imp. & p. p. Appreciated;
   p. pr. & vb. n. Appreciating.] [L. appretiatus, p. p. of
   appretiare to value at a price, appraise; ad + pretiare to
   prize, pretium price. Cf. Appraise.]
   1. To set a price or value on; to estimate justly; to value.
      [1913 Webster]

            To appreciate the motives of their enemies.
                                                  --Gibbon.
      [1913 Webster]

   3. To raise the value of; to increase the market price of; --
      opposed to depreciate. [U.S.]
      [1913 Webster]

            Lest a sudden peace should appreciate the money.
                                                  --Ramsay.
      [1913 Webster]

   4. To be sensible of; to distinguish.
      [1913 Webster]

            To test the power of bees to appreciate color.
                                                  --Lubbock.
      [1913 Webster]

   Syn: To Appreciate, Estimate, Esteem.

   Usage: Estimate is an act of judgment; esteem is an act of
          valuing or prizing, and when applied to individuals,
          denotes a sentiment of moral approbation. See
          Estimate. Appreciate lies between the two. As
          compared with estimate, it supposes a union of
          sensibility with judgment, producing a nice and
          delicate perception. As compared with esteem, it
          denotes a valuation of things according to their
          appropriate and distinctive excellence, and not simply
          their moral worth. Thus, with reference to the former
          of these (delicate perception), an able writer says.
          "Women have a truer appreciation of character than
          men;" and another remarks, "It is difficult to
          appreciate the true force and distinctive sense of
          terms which we are every day using." So, also, we
          speak of the difference between two things, as
          sometimes hardly appreciable. With reference to the
          latter of these (that of valuation as the result of a
          nice perception), we say, "It requires a peculiar cast
          of character to appreciate the poetry of Wordsworth;"
          "He who has no delicacy himself, can not appreciate it
          in others;" "The thought of death is salutary, because
          it leads us to appreciate worldly things aright."
          Appreciate is much used in cases where something is in
          danger of being overlooked or undervalued; as when we
          speak of appreciating the difficulties of a subject,
          or the risk of an undertaking. So Lord Plunket,
          referring to an "ominous silence" which prevailed
          among the Irish peasantry, says, "If you knew how to
          appreciate that silence, it is more formidable than
          the most clamorous opposition." In like manner, a
          person who asks some favor of another is apt to say,
          "I trust you will appreciate my motives in this
          request." Here we have the key to a very frequent use
          of the word. It is hardly necessary to say that
          appreciate looks on the favorable side of things. we
          never speak of appreciating a man's faults, but his
          merits. This idea of regarding things favorably
          appears more fully in the word appreciative; as when
          we speak of an appreciative audience, or an
          appreciative review, meaning one that manifests a
          quick perception and a ready valuation of excellence.
          [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Appreciate \Ap*pre"ci*ate\, v. i.
   To rise in value. [See note under Rise, v. i.] --J. Morse.
   [1913 Webster]

WordNet (r) 3.0 (2006):

appreciate
    v 1: recognize with gratitude; be grateful for
    2: be fully aware of; realize fully; "Do you appreciate the full
       meaning of this letter?" [syn: appreciate, take account]
    3: hold dear; "I prize these old photographs" [syn: prize,
       value, treasure, appreciate]
    4: gain in value; "The yen appreciated again!" [syn:
       appreciate, apprize, apprise, revalue] [ant:
       depreciate, devaluate, devalue, undervalue]
    5: increase the value of; "The Germans want to appreciate the
       Deutsche Mark" [syn: appreciate, apprize, apprise]
       [ant: depreciate]

Moby Thesaurus II by Grady Ward, 1.0:

198 Moby Thesaurus words for "appreciate":
   absorb, accord respect to, accrue, accumulate, admire, adore,
   advance, apotheosize, appraise, apprehend, apprize,
   ascribe importance to, assay, assess, assimilate, balloon, bask in,
   be acquainted with, be appreciative of, be apprised of,
   be aware of, be cognizant of, be conscious of, be conversant with,
   be fond of, be grateful, be indebted, be informed, be obligated,
   be obliged, be partial to, be pleased with, be thankful,
   be with one, bloat, boom, breed, broaden, calculate, calibrate,
   caliper, call, catch, catch on, check a parameter, cherish, class,
   cognize, comprehend, compute, conceive, conceptualize, crescendo,
   defer to, deify, delight, delight in, derive pleasure from,
   develop, devour, dial, dig, digest, discern, divide, eat up, enjoy,
   entertain respect for, esteem, estimate, evaluate, exalt, fathom,
   favor, feast on, figure, follow, form an estimate, freak out on,
   gain, gain strength, gauge, get, get ahead, get high on,
   get hold of, get the drift, get the idea, get the picture,
   give an appreciation, gloat over, go up, graduate, grasp,
   groove on, grow, guess, have, have information about,
   have it taped, have knowledge of, hero-worship, hold in esteem,
   hold in reverence, honor, idolize, increase, indulge in, intensify,
   ken, know, learn, like, look up to, love, luxuriate in,
   make an estimation, make much of, make out, mark, master, measure,
   mensurate, mete, meter, mount, multiply, never forget,
   overflow with gratitude, pace, perceive, plumb, possess, prehend,
   prize, probe, proliferate, quantify, quantize, rank, rate,
   rate highly, read, realize, reckon, recognize, regard, rejoice in,
   relish, respect, revel in, revere, reverence, riot in, rise,
   run up, savor, savvy, see, seize, seize the meaning, sense,
   set store by, shoot up, size, size up, smack the lips, snowball,
   sound, span, spread, step, strengthen, survey, swell, swim in,
   take, take a reading, take in, take pleasure in, taste, thank God,
   think highly of, think much of, think well of, treasure,
   triangulate, understand, valuate, value, venerate, wallow in, wax,
   weigh, widen, worship, wot, wot of