The Collaborative International Dictionary of English v.0.48:

Mad \Mad\, a. [Compar. Madder; superl. Maddest.] [AS. gem?d,
   gem[=a]d, mad; akin to OS. gem?d foolish, OHG. gameit, Icel.
   mei?a to hurt, Goth. gam['a]ids weak, broken. ?.]
   1. Disordered in intellect; crazy; insane.
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            I have heard my grandsire say full oft,
            Extremity of griefs would make men mad. --Shak.
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   2. Excited beyond self-control or the restraint of reason;
      inflamed by violent or uncontrollable desire, passion, or
      appetite; as, to be mad with terror, lust, or hatred; mad
      against political reform.
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            It is the land of graven images, and they are mad
            upon their idols.                     --Jer. 1. 88.
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            And being exceedingly mad against them, I persecuted
            them even unto strange cities.        --Acts xxvi.
                                                  11.
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   3. Proceeding from, or indicating, madness; expressing
      distraction; prompted by infatuation, fury, or extreme
      rashness. "Mad demeanor." --Milton.
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            Mad wars destroy in one year the works of many years
            of peace.                             --Franklin.
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            The mad promise of Cleon was fulfilled. --Jowett
                                                  (Thucyd.).
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   4. Extravagant; immoderate. "Be mad and merry." --Shak.
      "Fetching mad bounds." --Shak.
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   5. Furious with rage, terror, or disease; -- said of the
      lower animals; as, a mad bull; esp., having hydrophobia;
      rabid; as, a mad dog.
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   6. Angry; out of patience; vexed; as, to get mad at a person.
      [Colloq.]
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   7. Having impaired polarity; -- applied to a compass needle.
      [Colloq.]
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   Like mad, like a mad person; in a furious manner; as, to
      run like mad. --L'Estrange.

   To run mad.
      (a) To become wild with excitement.
      (b) To run wildly about under the influence of
          hydrophobia; to become affected with hydrophobia.

   To run mad after, to pursue under the influence of
      infatuation or immoderate desire. "The world is running
      mad after farce." --Dryden.
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WordNet (r) 3.0 (2006):

like mad
    adv 1: with great speed or effort or intensity; "drove like
           crazy"; "worked like hell to get the job done"; "ran like
           sin for the storm cellar"; "work like thunder"; "fought
           like the devil" [syn: like hell, like mad, like
           crazy, like sin, like thunder, like the devil]

Moby Thesaurus II by Grady Ward, 1.0:

58 Moby Thesaurus words for "like mad":
   a corps perdu, all to pieces, carelessly, demonically, desperately,
   fanatically, fiercely, frantically, frenetically, furiously,
   happen what may, hastily, head over heels, headfirst, headforemost,
   headlong, heedlessly, heels over head, helter-skelter, holus-bolus,
   hotheadedly, hotly, hurriedly, hurry-scurry, impetuously,
   like a flash, like a shot, like a streak, like blazes, like crazy,
   like fury, like greased lightning, like lightning,
   like one possessed, like sin, like sixty, madly, overeagerly,
   overenthusiastically, overzealously, precipitantly, precipitately,
   precipitously, ramble-scramble, recklessly, rigorously, severely,
   slam-bang, slap-bang, slapdash, uncontrollably, vehemently,
   venomously, violently, virulently, wantonly, wildly,
   with a vengeance