The Collaborative International Dictionary of English v.0.48:

Random \Ran"dom\, a.
   1. Going at random or by chance; done or made at hazard, or
      without settled direction, aim, or purpose; hazarded
      without previous calculation; left to chance; haphazard;
      as, a random guess.
      [1913 Webster]

            Some random truths he can impart.     --Wordsworth.
      [1913 Webster]

            So sharp a spur to the lazy, and so strong a bridle
            to the random.                        --H. Spencer.
      [1913 Webster]

   2. (Statistics) Of, pertaining to, or resulting from a
      process of selection from a starting set of items, in
      which the probability of selecting any one object in the
      starting set is equal to the probability of selecting any
      other.
      [PJC]

   3. (Construction) of unequal size or shape; made from
      components of unequal size or shape.
      [PJC]

   at random in a manner so that all possible results have an
      equal probability of occurrence; for processes, each
      possible result is counted separately although the same
      type of result may occur more than once .

   Random courses (Masonry), courses of stone of unequal
      thickness.

   Random shot, a shot not directed or aimed toward any
      particular object, or a shot with the muzzle of the gun
      much elevated.

   Random work (Masonry), stonework consisting of stones of
      unequal sizes fitted together, but not in courses nor
      always with flat beds.
      [1913 Webster]

WordNet (r) 3.0 (2006):

at random
    adv 1: in a random manner; "the houses were randomly scattered";
           "bullets were fired into the crowd at random" [syn:
           randomly, indiscriminately, haphazardly, willy-
           nilly, arbitrarily, at random, every which way]

Moby Thesaurus II by Grady Ward, 1.0:

63 Moby Thesaurus words for "at random":
   aimlessly, any which way, anyhow, anywise, around, at haphazard,
   at hazard, at intervals, at irregular intervals, brokenly,
   by catches, by chance, by fits, by jerks, by snatches,
   capriciously, carelessly, casually, desultorily, disconnectedly,
   discontinuously, dysteleologically, eccentrically, erratically,
   fitfully, haltingly, haphazard, haphazardly, helter-skelter,
   hit or miss, in snatches, in spots, inconstantly, indiscriminately,
   inexplicably, intermittently, irregularly, jerkily, lurchingly,
   nonuniformly, off and on, patchily, promiscuously, purposelessly,
   random, randomly, roughly, sloppily, spasmodically, sporadically,
   spottily, stochastically, unaccountably, uncertainly, unevenly,
   unmethodically, unpredictably, unrhythmically, unsteadily,
   unsystematically, variably, whimsically, wobblingly