The Collaborative International Dictionary of English v.0.48:

Droop \Droop\ (dr[=oo]p), v. i. [imp. & p. p. Drooped; p. pr.
   & vb. n. Drooping.] [Icel. dr[=u]pa; akin to E. drop. See
   Drop.]
   1. To hang bending downward; to sink or hang down, as an
      animal, plant, etc., from physical inability or
      exhaustion, want of nourishment, or the like. "The purple
      flowers droop." "Above her drooped a lamp." --Tennyson.
      [1913 Webster]

            I saw him ten days before he died, and observed he
            began very much to droop and languish. --Swift.
      [1913 Webster]

   2. To grow weak or faint with disappointment, grief, or like
      causes; to be dispirited or depressed; to languish; as,
      her spirits drooped.
      [1913 Webster]

            I'll animate the soldier's drooping courage.
                                                  --Addison.
      [1913 Webster]

   3. To proceed downward, or toward a close; to decline. "Then
      day drooped." --Tennyson.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Droop \Droop\, v. t.
   To let droop or sink. [R.] --M. Arnold.
   [1913 Webster]

         Like to a withered vine
         That droops his sapless branches to the ground. --Shak.
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Droop \Droop\, n.
   A drooping; as, a droop of the eye.
   [1913 Webster]

WordNet (r) 3.0 (2006):

droop
    n 1: a shape that sags; "there was a sag in the chair seat"
         [syn: sag, droop]
    v 1: droop, sink, or settle from or as if from pressure or loss
         of tautness [syn: sag, droop, swag, flag]
    2: hang loosely or laxly; "His tongue lolled" [syn: droop,
       loll]
    3: become limp; "The flowers wilted" [syn: wilt, droop]

Moby Thesaurus II by Grady Ward, 1.0:

184 Moby Thesaurus words for "droop":
   amble, bad, bag, become suicidal, blow, blue, break, break down,
   burn out, cadence, cascade, cast down, catenary, cave, cave in,
   collapse, come apart, come unstuck, conk out, couch, crack up,
   crumble, daggle, dangle, decline, decurrence, dejected, demit,
   depend, depress, depressed, desiccate, despair, despond,
   deteriorate, diminish, disintegrate, dispirited, doleful, down,
   downhearted, drabble, drag, draggle, drape, droopy, drop, dry up,
   dwindle, fade, fade away, fail, faint, fall, fatigue, fizzle out,
   flag, flap, flop, flop down, flounce, flow, flump, flump down,
   founder, gait, gallop, gasp, get tired, give out, give way,
   go down, go downhill, go soft, go to pieces, grow weary, hang,
   hang down, hit rock bottom, hit the skids, hitch, hobble, jade,
   jog, languish, lapse, let down, limp, lock step, loll, lollop, lop,
   lose heart, lose strength, lower, lowering, lurch, mince,
   mincing steps, nod, pace, paddle, pant, peak, peg out, pend,
   peter out, piaffer, pine, play out, plop, plop down,
   plumb the depths, plump, poop out, prance, puff, puff and blow,
   rack, reach the depths, roll, run down, run out, sag, saunter,
   scuttle, sear, set, settle, shrink, shrivel, shuffle, sidle,
   single-foot, sink, sink down, sinkage, sling, slink, slither,
   slouch, slowness, slump, slump down, stagger, stalk, step, stride,
   stroll, strolling gait, strut, submerge, submergence, subside,
   subsidence, succumb, suspend, swag, swagger, swing, tire, toddle,
   totter, touch bottom, trail, tread, trollop, trot, velocity,
   waddle, walk, waste, waste away, weaken, wear away, wear thin,
   weary, weep, wheeze, wilt, wither, wither away, wizen, yield