The Collaborative International Dictionary of English v.0.48:

Height \Height\ (h[imac]t), n. [Written also hight.] [OE.
   heighte, heght, heighthe, AS. he['a]h[eth]u, h[=e]h[eth]u fr.
   heah high; akin to D. hoogte, Sw. h["o]jd, Dan. h["o]ide,
   Icel. h[ae][eth], Goth. hauhi[thorn]a. See High.]
   1. The condition of being high; elevated position.
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            Behold the height of the stars, how high they are!
                                                  --Job xxii.
                                                  12.
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   2. The distance to which anything rises above its foot, above
      that on which in stands, above the earth, or above the
      level of the sea; altitude; the measure upward from a
      surface, as the floor or the ground, of an animal,
      especially of a man; stature. --Bacon.
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            [Goliath's] height was six cubits and a span. --1
                                                  Sam. xvii. 4.
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   3. Degree of latitude either north or south. [Obs.]
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            Guinea lieth to the north sea, in the same height as
            Peru to the south.                    --Abp. Abbot.
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   4. That which is elevated; an eminence; a hill or mountain;
      as, Alpine heights. --Dryden.
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   5. Elevation in excellence of any kind, as in power,
      learning, arts; also, an advanced degree of social rank;
      pre["e]minence or distinction in society; prominence.
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            Measure your mind's height by the shade it casts.
                                                  --R. Browning.
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            All would in his power hold, all make his subjects.
                                                  --Chapman.
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   6. Progress toward eminence; grade; degree.
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            Social duties are carried to greater heights, and
            enforced with stronger motives by the principles of
            our religion.                         --Addison.
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   7. Utmost degree in extent; extreme limit of energy or
      condition; as, the height of a fever, of passion, of
      madness, of folly; the height of a tempest.
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            My grief was at the height before thou camest.
                                                  --Shak.
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   On height, aloud. [Obs.]
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            [He] spake these same words, all on hight.
                                                  --Chaucer.
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WordNet (r) 3.0 (2006):

height
    n 1: the vertical dimension of extension; distance from the base
         of something to the top [syn: height, tallness]
    2: the highest level or degree attainable; the highest stage of
       development; "his landscapes were deemed the acme of beauty";
       "the artist's gifts are at their acme"; "at the height of her
       career"; "the peak of perfection"; "summer was at its peak";
       "...catapulted Einstein to the pinnacle of fame"; "the summit
       of his ambition"; "so many highest superlatives achieved by
       man"; "at the top of his profession" [syn: acme, height,
       elevation, peak, pinnacle, summit, superlative,
       meridian, tiptop, top]
    3: (of a standing person) the distance from head to foot [syn:
       stature, height]
    4: elevation especially above sea level or above the earth's
       surface; "the altitude gave her a headache" [syn: altitude,
       height]

Moby Thesaurus II by Grady Ward, 1.0:

228 Moby Thesaurus words for "height":
   French pitch, Olympian heights, acme, acme of perfection,
   aerial heights, altitude, amount, amplitude, apex, apogee,
   apotheosis, area, ascent, assumption, authority, authorization,
   be-all and end-all, beatification, bigness, blue ribbon, bluff,
   body, breadth, brow, bulk, caliber, canonization, cap,
   championship, classical pitch, cliff, climax, cloud nine, command,
   compass, consummation, control, coverage, crag, crest, crown,
   culmen, culmination, cut, degree, deification, depth, diameter,
   dimension, dimensions, directorship, dizzy heights, dominion, edge,
   effectiveness, elevation, eminence, enshrinement, erection,
   escalation, escarpment, ether, exaltation, expanse, expansion,
   extension, extent, extreme, extreme limit, extremity, fell,
   first place, first prize, gauge, girth, grade, greatness, headland,
   headship, heaven, heavens, hegemony, heights, high noon,
   high pitch, high point, highest, highest pitch, highest point,
   highness, hill, imperium, influence, interval, jurisdiction, key,
   kingship, largeness, last word, leadership, leap, length, level,
   lift, lifting, limit, loftiness, lordship, low pitch, magnitude,
   management, mark, mass, mastership, mastery, maximum, measure,
   measurement, meridian, most, mound, mountain, mountaintop,
   ne plus ultra, new high, new philharmonic pitch, no place higher,
   noon, notch, note, nuance, palms, paramountcy, pas, peak, peg,
   perfection, period, philharmonic pitch, philosophical pitch, pink,
   pink of perfection, pinnacle, pitch, plane, plateau, point, pole,
   power, presidency, primacy, prominence, promontory, proportion,
   proportions, radius, raise, raising, range, ratio, reach, rearing,
   record, register, remove, ridge, rise, rising ground, round, rule,
   rung, say, scale, scarp, scope, seventh heaven, shade, shadow,
   size, sky, sovereignty, space, spire, spread, stair, standard,
   standard pitch, stature, steep, step, stint, stratosphere, summit,
   supremacy, sursum corda, sway, tallness, tip, tip-top, tonality,
   tone, top, top spot, tor, tread, tune, ultimate, upbuoying, upcast,
   upheaval, uplift, uplifting, upmost, upper extremity, uppermost,
   upping, uprearing, uprise, upthrow, upthrust, utmost,
   vantage ground, vantage point, vertex, very top, volume, width,
   zenith