The Collaborative International Dictionary of English v.0.48:

Unaccountable \Un`ac*count"a*ble\, a.
   1. Not accountable or responsible; free from control.
      --South.
      [1913 Webster]

   2. Not to be accounted for; inexplicable; not consonant with
      reason or rule; strange; mysterious.
      [1913 Webster] -- Un`ac*count"a*ble*ness], n. --
      Un`ac*count"a*bly, adv.
      [1913 Webster]
      [1913 Webster]

WordNet (r) 3.0 (2006):

unaccountable
    adj 1: not to be accounted for or explained; "perceptible only
           as unaccountable influences that hinder progress"; "an
           unexplainable fear" [syn: unaccountable,
           unexplainable]
    2: free from control or responsibility

Moby Thesaurus II by Grady Ward, 1.0:

179 Moby Thesaurus words for "unaccountable":
   adrift, afloat, agnostic, aimless, alternating, ambiguous,
   amorphous, antic, baffling, bizarre, capricious, casual, causeless,
   chancy, changeable, changeful, chartered, designless, desultory,
   deviable, dicey, disobedient, dizzy, doubting, driftless,
   dysteleological, eccentric, enwrapped in mystery, equivocal,
   erratic, excepted, excused, exempt, exempted, extraordinary,
   fanciful, fantastic, fast and loose, favored, fickle, fitful,
   flickering, flighty, flitting, fluctuating, freakish, giddy,
   haphazard, headstrong, heady, hesitant, hesitating, immune,
   impetuous, impossible, impulsive, incalculable, incomprehensible,
   inconceivable, inconsistent, inconstant, incredible, indecisive,
   indefinable, indemonstrable, indiscriminate, inexplicable,
   inextricable, infirm, inscrutable, insoluble, insolvable,
   insubordinate, irregular, irresolute, irresponsible, lawless,
   let off, licensed, licentious, mazy, mercurial, mindless, moody,
   mutinous, mysterious, mystic, odd, peculiar, permitted, polysemous,
   privileged, promiscuous, purposeless, puzzling, rambling, rampant,
   random, reinless, released, restless, roving, scatterbrained,
   self-willed, shapeless, shifting, shifty, shuffling, skeptical,
   spared, spasmodic, spineless, stochastic, strange, stray,
   touch-and-go, unanswerable, unbelievable, unbridled, uncanny,
   uncertain, unchecked, unconfirmable, uncontrolled, unconvinced,
   uncurbed, undefinable, undependable, undirected, undisciplined,
   undivinable, unexpected, unexplainable, unexplained, unfathomable,
   unfixed, unforeseeable, ungoverned, unheard-of, unimaginable,
   unintelligible, uninterpretable, unliable, unmotivated, unorthodox,
   unpersuaded, unpredictable, unprovable, unreined, unreliable,
   unrestrained, unsettled, unsolvable, unstable, unstable as water,
   unstaid, unsteadfast, unsteady, unsubject, unsure, unusual,
   unverifiable, vacillating, vagrant, variable, vicissitudinary,
   vicissitudinous, volatile, wandering, wanton, wavering, wavery,
   wavy, wayward, weird, whimsical, wildcat, willful, wishy-washy