The Collaborative International Dictionary of English v.0.48:

Over \O"ver\ ([=o]"v[~e]r), prep. [AS. ofer; akin to D. over, G.
   ["u]ber, OHG. ubir, ubar, Dan. over, Sw. ["o]fver, Icel.
   yfir, Goth. ufar, L. super, Gr. "ype`r, Skr. upari.
   [root]199. Cf. Above, Eaves, Hyper-, Orlop, Super-,
   Sovereign, Up.]
   1. Above, or higher than, in place or position, with the idea
      of covering; -- opposed to under; as, clouds are over
      our heads; the smoke rises over the city.
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            The mercy seat that is over the testimony. --Ex.
                                                  xxx. 6.
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            Over them gleamed far off the crimson banners of
            morning.                              --Longfellow.
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   2. Across; from side to side of; -- implying a passing or
      moving, either above the substance or thing, or on the
      surface of it; as, a dog leaps over a stream or a table.
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            Certain lakes . . . poison birds which fly over
            them.                                 --Bacon.
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   3. Upon the surface of, or the whole surface of; hither and
      thither upon; throughout the whole extent of; as, to
      wander over the earth; to walk over a field, or over a
      city.
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   4. Above; -- implying superiority in excellence, dignity,
      condition, or value; as, the advantages which the
      Christian world has over the heathen. --Swift.
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   5. Above in authority or station; -- implying government,
      direction, care, attention, guard, responsibility, etc.;
      -- opposed to under.
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            Thou shalt be over my house.          --Gen. xli.
                                                  40.
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            I will make thee rules over many things. --Matt.
                                                  xxv. 23.
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            Dost thou not watch over my sin ?     --Job xiv. 16.
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            His tender mercies are over all his works. --Ps.
                                                  cxlv. 9.
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   6. Across or during the time of; from beginning to end of;
      as, to keep anything over night; to keep corn over winter.
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   7. Above the perpendicular height or length of, with an idea
      of measurement; as, the water, or the depth of water, was
      over his head, over his shoes.
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   8. Beyond; in excess of; in addition to; more than; as, it
      cost over five dollars. "Over all this." --Chaucer.
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   9. Above, implying superiority after a contest; in spite of;
      notwithstanding; as, he triumphed over difficulties; the
      bill was passed over the veto.
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   Note: Over, in poetry, is often contracted into o'er.
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   Note: Over his signature (or name) is a substitute for the
         idiomatic English form, under his signature (name, hand
         and seal, etc.), the reference in the latter form being
         to the authority under which the writing is made,
         executed, or published, and not the place of the
         autograph, etc.
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   Over all (Her.), placed over or upon other bearings, and
      therefore hinding them in part; -- said of a charge.

   Over one's head, Over head and ears, beyond one's depth;
      completely; wholly; hopelessly; as, over head and ears in
      debt.

   head over heels
      (a) completely; intensely; as, head over heels in love.
          [Colloq.]
      (b) in a tumbling manner; as, to fall head over heels down
          the stairs.
      (c) precipitously and without forethought; impulsively.

   Over the left. See under Left.

   To run over (Mach.), to have rotation in such direction
      that the crank pin traverses the upper, or front, half of
      its path in the forward, or outward, stroke; -- said of a
      crank which drives, or is driven by, a reciprocating
      piece.
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WordNet (r) 3.0 (2006):

head over heels
    adv 1: in disorderly haste; "we ran head over heels toward the
           shelter" [syn: head over heels, heels over head,
           topsy-turvy, topsy-turvily, in great confusion]

Moby Thesaurus II by Grady Ward, 1.0:

81 Moby Thesaurus words for "head over heels":
   a corps perdu, abruptly, anticlockwise, around, arsy-varsy,
   ass over elbows, back-to-front, backwards, bottom side up,
   bottom up, capsized, carelessly, chiastic, clockwise, contrarily,
   contrariwise, conversely, counterclockwise, desperately, everted,
   furiously, happen what may, hastily, headfirst, headforemost,
   headlong, heedlessly, heels over head, helter-skelter, holus-bolus,
   hotheadedly, hurriedly, hurry-scurry, hyperbatic, impetuously,
   impulsively, in a circle, in a spin, in a whirl, in circles,
   inside out, introverted, invaginated, inversed, inversely,
   inverted, like crazy, like mad, madly, outside in, over,
   overeagerly, overenthusiastically, overzealously, palindromic,
   precipitantly, precipitately, precipitously, ramble-scramble,
   rashly, recklessly, resupinate, retroverted, reversed, round,
   round about, round and round, slam-bang, slap-bang, slapdash,
   suddenly, topsy-turvy, transposed, turned around, upside down,
   upside-down, vice versa, wantonly, widdershins, wildly,
   wrong side out