The Collaborative International Dictionary of English v.0.48:

Extremity \Ex*trem"i*ty\, n.; pl. Extremities. [L. extremitas:
   cf. F. extr['e]mit['e].]
   1. The extreme part; the utmost limit; the farthest or
      remotest point or part; as, the extremities of a country.
      [1913 Webster]

            They sent fleets . . . to the extremities of
            Ethiopia.                             --Arbuthnot.
      [1913 Webster]

   2. (Zo["o]l.) One of locomotive appendages of an animal; a
      limb; a leg or an arm of man.
      [1913 Webster]

   3. The utmost point; highest degree; most aggravated or
      intense form. "The extremity of bodily pain." --Ray.
      [1913 Webster]

   4. The highest degree of inconvenience, pain, or suffering;
      greatest need or peril; extreme need; necessity.
      [1913 Webster]

            Divers evils and extremities that follow upon such a
            compulsion shall here be set in view. --Milton.
      [1913 Webster]

            Upon mere extremity he summoned this last
            Parliament.                           --Milton.

   Syn: Verge; border; extreme; end; termination.
        [1913 Webster]

WordNet (r) 3.0 (2006):

extremity
    n 1: an external body part that projects from the body; "it is
         important to keep the extremities warm" [syn: extremity,
         appendage, member]
    2: an extreme condition or state (especially of adversity or
       disease)
    3: the greatest or utmost degree; "the extremity of despair"
    4: the outermost or farthest region or point
    5: that part of a limb that is farthest from the torso

Moby Thesaurus II by Grady Ward, 1.0:

339 Moby Thesaurus words for "extremity":
   Thule, Ultima Thule, abandon, abstract, aching heart, acme,
   acuteness, agony, agony of mind, all, anguish, animality, apex,
   apogee, arch, arms, atrocity, bale, barbarity, bitter end,
   bitterness, bleeding heart, blind alley, bloodlust, border,
   border line, bottom dollar, bound, boundary, boundary condition,
   boundary line, boundlessness, bounds, bourn, box, break boundary,
   breakoff point, broken heart, brow, brutality, butt, butt end, cap,
   ceiling, circumscription, clear, clear away, climacteric, climax,
   cloud nine, clubfoot, clutch, compass, confine,
   convergence of events, corner, crest, crisis, critical juncture,
   critical point, crossroads, crown, crucial period, crunch,
   crushing, cul-de-sac, culmen, culmination, cutoff, cutoff point,
   dead end, dead-end street, deadline, deadlock, death agonies,
   death groan, death rattle, death struggle, death throes, deathbed,
   deathwatch, delimitation, deliver, depression, depth of misery,
   desolation, despair, destructiveness, detach, determinant,
   difference, differentiate, digit, disburden, discern, discriminate,
   disembarrass, disembroil, disencumber, disengage, disentangle,
   disinvolve, distinguish, division line, dog, dying breath, edge,
   egregiousness, emergency, end, enormousness, exaggeration, excess,
   excessiveness, exigency, exorbitance, exorbitancy, extravagance,
   extravagancy, extreme, extreme limit, extremes, extremism,
   extremities, extricate, fabulousness, fag end, farthest bound,
   feet, ferociousness, fetlock, fierceness, final extremity, fingers,
   finish, floor, foot, force, forefoot, forepaw, free, frontier,
   furiousness, giantism, gigantism, gluttony, grief, halt, hands,
   harefoot, harshness, heartache, heaven, heavens, heavy heart,
   hedge, heel, height, high noon, high-water mark, highest degree,
   highest pitch, highest point, hinge, hole, hoof, hyperbole,
   hypertrophy, immoderacy, immoderateness, immoderation, impasse,
   impetuosity, inclemency, incontinence, infelicity, inhumanity,
   inordinacy, inordinance, inordinateness, instep, intemperance,
   intemperateness, intensity, interface, jumping-off place,
   last agony, last breath, last gasp, legs, liberate, limbs, limen,
   limit, limitation, limiting factor, limits, line,
   line of demarcation, low-water mark, lower limit, malignity, march,
   margin, mark, maximum, melancholia, melancholy, mercilessness,
   meridian, mete, mindlessness, misery, monstrousness, moribundity,
   mountaintop, murderousness, ne plus ultra, nib, nimiety,
   no place higher, noon, nth degree, outrageousness, overdevelopment,
   overgreatness, overgrowth, overindulgence, overlargeness, overmuch,
   overmuchness, pad, pass, pastern, patte, paw, peak,
   pedal extremity, pedes, periphery, pes, pied, pinch, pinnacle,
   pitch, pitilessness, point, pole, prostration, pug, push,
   radicalism, release, rescue, resolve, ridge, rigor, roughness, rub,
   sadness, savagery, separate, seventh heaven, sever, severalize,
   severity, sharpness, sky, sole, spire, splayfoot, stalemate, stand,
   standstill, start, starting line, starting point, stop, strait,
   stub, stump, suicidal despair, summit, tag, tag end, tail,
   tail end, target date, term, terminal date, termination, terminus,
   terrorism, the whole, threshold, throes of death, time allotment,
   tip, tip-top, toe, toes, too much, too-muchness, tootsy, top,
   trotter, trotters, turn, turning point, unconscionableness,
   undueness, ungentleness, ungula, unravel, unreasonableness,
   unrestrainedness, unscramble, untangle, untie, untwine, upmost,
   upper extremity, upper limit, uppermost, utmost, utmost extent,
   uttermost, vandalism, vehemence, venom, vertex, very top,
   viciousness, violence, virulence, wings, woe, wretchedness,
   zenith