The Collaborative International Dictionary of English v.0.48:

Great \Great\ (gr[=a]t), a. [Compar. Greater; superl.
   Greatest.] [OE. gret, great, AS. gre['a]t; akin to OS. &
   LG. gr[=o]t, D. groot, OHG. gr[=o]z, G. gross. Cf. Groat
   the coin.]
   1. Large in space; of much size; big; immense; enormous;
      expanded; -- opposed to small and little; as, a great
      house, ship, farm, plain, distance, length.
      [1913 Webster]

   2. Large in number; numerous; as, a great company, multitude,
      series, etc.
      [1913 Webster]

   3. Long continued; lengthened in duration; prolonged in time;
      as, a great while; a great interval.
      [1913 Webster]

   4. Superior; admirable; commanding; -- applied to thoughts,
      actions, and feelings.
      [1913 Webster]

   5. Endowed with extraordinary powers; uncommonly gifted; able
      to accomplish vast results; strong; powerful; mighty;
      noble; as, a great hero, scholar, genius, philosopher,
      etc.
      [1913 Webster]

   6. Holding a chief position; elevated: lofty: eminent;
      distinguished; foremost; principal; as, great men; the
      great seal; the great marshal, etc.
      [1913 Webster]

            He doth object I am too great of birth. --Shak.
      [1913 Webster]

   7. Entitled to earnest consideration; weighty; important; as,
      a great argument, truth, or principle.
      [1913 Webster]

   8. Pregnant; big (with young).
      [1913 Webster]

            The ewes great with young.            --Ps. lxxviii.
                                                  71.
      [1913 Webster]

   9. More than ordinary in degree; very considerable in degree;
      as, to use great caution; to be in great pain.
      [1913 Webster]

            We have all
            Great cause to give great thanks.     --Shak.
      [1913 Webster]

   10. (Genealogy) Older, younger, or more remote, by single
       generation; -- often used before grand to indicate one
       degree more remote in the direct line of descent; as,
       great-grandfather (a grandfather's or a grandmother's
       father), great-grandson, etc.
       [1913 Webster]

   Great bear (Astron.), the constellation Ursa Major.

   Great cattle (Law), all manner of cattle except sheep and
      yearlings. --Wharton.

   Great charter (Eng. Hist.), Magna Charta.

   Great circle of a sphere, a circle the plane of which
      passes through the center of the sphere.

   Great circle sailing, the process or art of conducting a
      ship on a great circle of the globe or on the shortest arc
      between two places.

   Great go, the final examination for a degree at the
      University of Oxford, England; -- called also greats.
      --T. Hughes.

   Great guns. (Naut.) See under Gun.

   The Great Lakes the large fresh-water lakes (Lakes
      Superior, Michigan, Huron, Erie, and Ontario) which lie on
      the northern borders of the United States.

   Great master. Same as Grand master, under Grand.

   Great organ (Mus.), the largest and loudest of the three
      parts of a grand organ (the others being the choir organ
      and the swell, and sometimes the pedal organ or foot
      keys), It is played upon by a separate keyboard, which has
      the middle position.

   The great powers (of Europe), in modern diplomacy, Great
      Britain, France, Germany, Austria, Russia, and Italy.

   Great primer. See under Type.

   Great scale (Mus.), the complete scale; -- employed to
      designate the entire series of musical sounds from lowest
      to highest.

   Great sea, the Mediterranean sea. In Chaucer both the Black
      and the Mediterranean seas are so called.

   Great seal.
       (a) The principal seal of a kingdom or state.
       (b) In Great Britain, the lord chancellor (who is
           custodian of this seal); also, his office.

   Great tithes. See under Tithes.

   The great, the eminent, distinguished, or powerful.

   The Great Spirit, among the North American Indians, their
      chief or principal deity.

   To be great (with one), to be intimate or familiar (with
      him). --Bacon.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

greatest \greatest\ adj. [superl. of great.]
   1. not to be surpassed.

   Syn: top.
        [WordNet 1.5]

   2. largest in size of those under consideration.

   Syn: biggest, largest.
        [WordNet 1.5]

   3. most of.
      [WordNet 1.5]

   4. highest in importance or degree or significance or
      achievement; most eminent; as, our greatest statesmen.

   Syn: leading(prenominal), preeminent.
        [WordNet 1.5]

   5. highest in quality.

   Syn: sterling(prenominal), superlative.
        [WordNet 1.5]

WordNet (r) 3.0 (2006):

greatest
    adj 1: highest in quality [syn: greatest, sterling(a),
           superlative]

Moby Thesaurus II by Grady Ward, 1.0:

48 Moby Thesaurus words for "greatest":
   at the height, at the limit, best, champion, choice, elect, elite,
   extreme, far out, first-class, first-rate, for the best, furthest,
   handpicked, highest, matchless, maximal, maximum, most, optimal,
   optimum, paramount, peerless, picked, prime, prize, quintessential,
   radical, select, superlative, supreme, surpassing, tip-top,
   too much, top, top-notch, topmost, ultra, ultra-ultra, unmatchable,
   unmatched, unparalleled, unsurpassed, uppermost, utmost, uttermost,
   very best, way out