The Collaborative International Dictionary of English v.0.48:

Negligent \Neg"li*gent\, a. [F. n['e]gligent, L. negligens,p.
   pr. of negligere. See Neglect.]
   Apt to neglect; customarily neglectful; characterized by
   negligence; careless; heedless; culpably careless; showing
   lack of attention; as, disposed in negligent order. "Be thou
   negligent of fame." --Swift.
   [1913 Webster]

         He that thinks he can afford to be negligent is not far
         from being poor.                         --Rambler.
   [1913 Webster]

   Syn: Careles; heedless; neglectful; regardless; thoughtless;
        indifferent; inattentive; remiss.
        [1913 Webster]

WordNet (r) 3.0 (2006):

negligent
    adj 1: characterized by neglect and undue lack of concern;
           "negligent parents"; "negligent of detail"; "negligent in
           his correspondence" [ant: diligent]

Moby Thesaurus II by Grady Ward, 1.0:

170 Moby Thesaurus words for "negligent":
   apathetic, approximate, approximative, ataractic, beat-up,
   bedraggled, behindhand, blase, blowzy, botched, bungled, butchered,
   careless, casual, chintzy, culpably negligent, delinquent,
   derelict, devil-may-care, dilapidated, disinterested,
   dispassionate, disregardant, disregardful, distracted, distrait,
   drabbletailed, draggled, draggletailed, easy, easygoing, feckless,
   frowzy, frumpish, frumpy, fumbled, grasshopper, grubby,
   happy-go-lucky, heedless, ill-advised, ill-considered,
   ill-contrived, ill-devised, ill-done, ill-executed, ill-managed,
   impolitic, impotent, imprecise, improvident, in rags, inaccurate,
   inadvertent, inattentive, inconsiderate, inconstant, incorrect,
   incurious, indifferent, inexact, inexcitable, informal,
   inobservant, insouciant, lackadaisical, laissez-faire, lax,
   lenient, listless, loose, lumpen, messy, mindless, misconducted,
   misdirected, misguided, mismanaged, muffed, murdered, mussy,
   neglectful, neglecting, nonadherent, nonchalant, noncompliant,
   nonconforming, noninterfering, nonobservant, nonrestrictive,
   off-guard, out of line, out of plumb, out of square, out of true,
   overindulgent, overly permissive, overpermissive, perfunctory,
   permissive, pococurante, poky, procrastinating, ragged, raggedy,
   reckless, regardless, relaxed, remiss, ruinous, scamping, scraggly,
   seedy, shabby, shiftless, shoddy, skimping, slack, slatternly,
   slighting, slipshod, sloppy, slovenly, slurring, sluttish, soft,
   sordid, spoiled, squalid, tacky, tattered, thoughtless, thriftless,
   turned-off, unanxious, uncircumspect, uncompliant, unconcerned,
   unconforming, undiscriminating, uneconomical, unfactual,
   unfaithful, unguarded, unheedful, unheeding, uninterested, unkempt,
   unloyal, unmarking, unmindful, unneat, unnoticing, unnoting,
   unobservant, unobserving, unprecise, unproviding, unremarking,
   unrestrained, unrigorous, unsightly, unsolicitous, unthinking,
   unthrifty, untidy, untrue, unwary, unwatchful, weak