The Collaborative International Dictionary of English v.0.48:

Sigh \Sigh\, v. i. [imp. & p. p. Sighed; p. pr. & vb. n.
   Sighing.] [OE. sighen, si?en; cf. also OE. siken, AS.
   s[imac]can, and OE. sighten, si?ten, sichten, AS. siccettan;
   all, perhaps, of imitative origin.]
   1. To inhale a larger quantity of air than usual, and
      immediately expel it; to make a deep single audible
      respiration, especially as the result or involuntary
      expression of fatigue, exhaustion, grief, sorrow, or the
      like.
      [1913 Webster]

   2. Hence, to lament; to grieve.
      [1913 Webster]

            He sighed deeply in his spirit.       --Mark viii.
                                                  12.
      [1913 Webster]

   3. To make a sound like sighing.
      [1913 Webster]

            And the coming wind did roar more loud,
            And the sails did sigh like sedge.    --Coleridge.
      [1913 Webster]

            The winter winds are wearily sighing. --Tennyson.
      [1913 Webster]

   Note: An extraordinary pronunciation of this word as
         s[imac]th is still heard in England and among the
         illiterate in the United States.
         [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Sigh \Sigh\, v. t.
   1. To exhale (the breath) in sighs.
      [1913 Webster]

            Never man sighed truer breath.        --Shak.
      [1913 Webster]

   2. To utter sighs over; to lament or mourn over.
      [1913 Webster]

            Ages to come, and men unborn,
            Shall bless her name, and sigh her fate. --Pior.
      [1913 Webster]

   3. To express by sighs; to utter in or with sighs.
      [1913 Webster]

            They . . . sighed forth proverbs.     --Shak.
      [1913 Webster]

            The gentle swain . . . sighs back her grief.
                                                  --Hoole.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Sigh \Sigh\, n. [OE. sigh; cf. OE. sik. See Sigh, v. i.]
   1. A deep and prolonged audible inspiration or respiration of
      air, as when fatigued or grieved; the act of sighing.
      [1913 Webster]

            I could drive the boat with my sighs. --Shak.
      [1913 Webster]

   2. Figuratively, a manifestation of grief; a lan?ent.
      [1913 Webster]

            With their sighs the air
            Frequenting, sent from hearts contrite. --Milton.
      [1913 Webster]

WordNet (r) 3.0 (2006):

sigh
    n 1: an utterance made by exhaling audibly [syn: sigh,
         suspiration]
    2: a sound like a person sighing; "she heard the sigh of the
       wind in the trees"
    v 1: heave or utter a sigh; breathe deeply and heavily; "She
         sighed sadly" [syn: sigh, suspire]
    2: utter with a sigh

Moby Thesaurus II by Grady Ward, 1.0:

160 Moby Thesaurus words for "sigh":
   Aqua-Lung, ache, artificial respiration, aspirate, aspiration,
   asthmatic wheeze, bark, bated breath, bawl, bellow, bemoan, bewail,
   blare, blat, blow, blubber, boom, bray, breath, breath of air,
   breathe, breathe hard, breathe in, breathe out, breathing,
   breathy voice, broken wind, buzz, cackle, chant, chirp, coo, cough,
   crave, crow, deplore, dirge, drawl, dream, elegize, exclaim,
   exhalation, exhale, exhaust, expel, expiration, expire,
   exsufflation, flute, gasp, give sorrow words, grieve, groan, growl,
   grunt, gulp, hack, hanker, hiccup, hiss, howl, huff, hunger,
   inhalation, inhalator, inhale, inspiration, inspire, insufflation,
   iron lung, keen, knell, lament, lilt, little voice, low voice,
   lust, maffle, moan, moaning, mourn, mouth-to-mouth resuscitation,
   mumble, mumbling, murmur, murmuration, murmuring, mussitate,
   mutter, muttering, oxygen mask, oxygen tent, pant, pine, pine for,
   pipe, puff, repine, respiration, respire, roar, rumble, scream,
   screech, scuba, shriek, sibilate, sigh for, sighing, sing,
   sing the blues, snap, snarl, sneeze, sniff, sniffle, snore,
   snoring, snort, snuff, snuffle, sob, sobbing, sock, soft voice,
   sorrow, sough, soughing, sound, squall, squawk, squeal,
   stage whisper, sternutation, stertor, still small voice,
   suspiration, susurrate, susurration, susurrus, thunder, trumpet,
   twang, underbreath, undertone, wail, warble, weep over, wheeze,
   whine, whining, whisper, whispering, whistle, wind, yap, yawp,
   yearn for, yell, yelp