The Collaborative International Dictionary of English v.0.48:

Despair \De*spair"\, v. i. [imp. & p. p. Despaired; p. pr. &
   vb. n. Despairing.] [OE. despeiren, dispeiren, OF.
   desperer, fr. L. desperare; de- + sperare to hope; akin to
   spes hope, and perh. to spatium space, E. space, speed; cf.
   OF. espeir hope, F. espoir. Cf. Prosper, Desperate.]
   To be hopeless; to have no hope; to give up all hope or
   expectation; -- often with of.
   [1913 Webster]

         We despaired even of life.               --2 Cor. i. 8.
   [1913 Webster]

         Never despair of God's blessings here.   --Wake.

   Syn: See Despond.
        [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Despair \De*spair"\, v. t.
   1. To give up as beyond hope or expectation; to despair of.
      [Obs.]
      [1913 Webster]

            I would not despair the greatest design that could
            be attempted.                         --Milton.
      [1913 Webster]

   2. To cause to despair. [Obs.] --Sir W. Williams.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Despair \De*spair"\, n. [Cf. OF. despoir, fr. desperer.]
   1. Loss of hope; utter hopelessness; complete despondency.
      [1913 Webster]

            We in dark dreams are tossing to and fro,
            Pine with regret, or sicken with despair. --Keble.
      [1913 Webster]

            Before he [Bunyan] was ten, his sports were
            interrupted by fits of remorse and despair.
                                                  --Macaulay.
      [1913 Webster]

   2. That which is despaired of. "The mere despair of surgery
      he cures." --Shak.

   Syn: Desperation; despondency; hopelessness.
        [1913 Webster]

WordNet (r) 3.0 (2006):

despair
    n 1: a state in which all hope is lost or absent; "in the depths
         of despair"; "they were rescued from despair at the last
         minute"; "courage born of desperation" [syn: despair,
         desperation]
    2: the feeling that everything is wrong and nothing will turn
       out well; "they moaned in despair and dismay"; "one harsh
       word would send her into the depths of despair" [ant: hope]
    v 1: abandon hope; give up hope; lose heart; "Don't despair--
         help is on the way!" [ant: hope]

Moby Thesaurus II by Grady Ward, 1.0:

98 Moby Thesaurus words for "despair":
   Schmerz, Slough of Despond, abandon, abandon hope, acedia,
   aching heart, agony, agony of mind, anguish, apathy, bale,
   become suicidal, bitterness, blank despondency, bleeding heart,
   broken heart, cave of Trophonius, cave of despair, crushing,
   death wish, dejectedness, dejection, depression, depth of misery,
   desolation, despair of, desperateness, desperation, despond,
   despondency, despondentness, disconsolateness, discouragement,
   disheartenment, dispiritedness, distress, down trip, downcastness,
   downer, downheartedness, droop, drooping spirits, drop, extremity,
   falter, forlornness, give up, give up hope, give way, gloom,
   gloominess, grief, heartache, heartlessness, heavy heart,
   hit rock bottom, hopelessness, infelicity, languish, lose heart,
   lose hope, low spirits, lowness, lowness of spirit, malaise,
   melancholia, melancholy, miserableness, misery, no exit, no way,
   no way out, oppression, pessimism, plumb the depths, prostration,
   quit, reach the depths, relinquish, renounce, resign, resignation,
   sadness, self-destructive urge, sink, sink into despair,
   sinking heart, sloth, spiritlessness, suicidal despair, surrender,
   taedium vitae, touch bottom, weariness of life, woe, wretchedness,
   yield, yield to despair