The Collaborative International Dictionary of English v.0.48:

Forgetful \For*get"ful\, a.
   1. Apt to forget; easily losing remembrance; as, a forgetful
      man should use helps to strengthen his memory.
      [1913 Webster]

   2. Heedless; careless; neglectful; inattentive.
      [1913 Webster]

            Be not forgetful to entertain strangers. --Heb.
                                                  xiii. 2.
      [1913 Webster]

   3. Causing to forget; inducing oblivion; oblivious. [Archaic
      or Poetic] "The forgetful wine." --J. Webster.
      [1913 Webster]

WordNet (r) 3.0 (2006):

forgetful
    adj 1: (of memory) deficient in retentiveness or range; "a short
           memory" [syn: unretentive, forgetful, short] [ant:
           long, recollective, retentive, tenacious]
    2: not mindful or attentive; "while thus unmindful of his steps
       he stumbled"- G.B.Shaw [syn: unmindful, forgetful,
       mindless] [ant: aware, mindful]
    3: failing to keep in mind; "forgetful of her responsibilities";
       "oblivious old age" [syn: forgetful, oblivious]

Moby Thesaurus II by Grady Ward, 1.0:

67 Moby Thesaurus words for "forgetful":
   Lethean, absent, absent-minded, absentminded, abstracted, airy,
   amnesiac, amnestic, bemused, blocked, careless, casual, converted,
   cursory, degage, disregardant, disregardful, distracted, dreaming,
   dreamy, easygoing, flippant, forgetting, free and easy, heedless,
   in the clouds, inattentive, inclined to forget, inconsiderate,
   indifferent, insouciant, lax, lazy, mindless, neglectful,
   negligent, oblivious, offhand, out of it, perfunctory, preoccupied,
   reckless, regardless, remiss, remote, repressed, respectless,
   slack, suppressed, tactless, thoughtless, unaccommodating,
   uncomplaisant, uncooperative, undiplomatic, unheedful, unheeding,
   unhelpful, unmindful, unobliging, unprepared, unready,
   unsolicitous, untactful, unthinking, unthoughtful, unwitting