The Collaborative International Dictionary of English v.0.48:

Approve \Ap*prove"\, v. t. [imp. & p. p. Approved; p. pr. &
   vb. n. Approving.] [OE. aproven, appreven, to prove, OF.
   aprover, F. approuver, to approve, fr. L. approbare; ad +
   probare to esteem as good, approve, prove. See Prove, and
   cf. Approbate.]
   1. To show to be real or true; to prove. [Obs.]
      [1913 Webster]

            Wouldst thou approve thy constancy? Approve
            First thy obedience.                  --Milton.
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   2. To make proof of; to demonstrate; to prove or show
      practically.
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            Opportunities to approve . . . worth. --Emerson.
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            He had approved himself a great warrior. --Macaulay.
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            'T is an old lesson; Time approves it true. --Byron.
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            His account . . . approves him a man of thought.
                                                  --Parkman.
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   3. To sanction officially; to ratify; to confirm; as, to
      approve the decision of a court-martial.
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   4. To regard as good; to commend; to be pleased with; to
      think well of; as, we approve the measured of the
      administration.
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   5. To make or show to be worthy of approbation or acceptance.
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            The first care and concern must be to approve
            himself to God.                       --Rogers.
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   Note: This word, when it signifies to be pleased with, to
         think favorably (of), is often followed by of.
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               They had not approved of the deposition of James.
                                                  --Macaulay.
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               They approved of the political institutions. --W.
                                                  Black.
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The Collaborative International Dictionary of English v.0.48:

Approve \Ap*prove"\ ([a^]p*pr[=oo]v"), v. t. [OF. aprouer; a (L.
   ad) + a form apparently derived fr. the pro, prod, in L.
   prodest it is useful or profitable, properly the preposition
   pro for. Cf. Improve.] (Eng. Law)
   To make profit of; to convert to one's own profit; -- said
   esp. of waste or common land appropriated by the lord of the
   manor.
   [1913 Webster]

WordNet (r) 3.0 (2006):

approve
    v 1: give sanction to; "I approve of his educational policies"
         [syn: approve, O.K., okay, sanction] [ant:
         disapprove, reject]
    2: judge to be right or commendable; think well of [ant:
       disapprove]

Moby Thesaurus II by Grady Ward, 1.0:

139 Moby Thesaurus words for "approve":
   OK, accede to, accept, accord to, accredit, admire, adopt,
   affiliate, affirm, agree to, allow, amen, applaud, approve of,
   argue, assent, assent to, attest, authenticate, authorize,
   autograph, back up, be partial to, be willing, bear, bespeak,
   betoken, bless, breathe, carry, certify, clear, commend,
   compliment, condescend, condone, confirm, connive at, connote,
   consent, consent to silently, cosign, countenance, countersign,
   deign, demonstrate, denote, display, embrace, endorse, endure,
   espouse, esteem, evidence, evince, exhibit, express, favor,
   furnish evidence, give consent, give indication of,
   give permission, give the go-ahead, give the imprimatur,
   give thumbs up, go along with, go for, go in for, go to show,
   grant, have no objection, have regard for, hold with, illustrate,
   imply, indicate, initial, involve, keep in countenance, like,
   manifest, mark, nod, nod assent, not refuse, notarize, okay, pass,
   pass on, pass upon, permit, point to, put up with, ratify,
   recommend, respect, rubber stamp, rubber-stamp, sanction,
   say amen to, say aye, say yes, seal, second, set forth, show,
   show signs of, sign, sign and seal, signalize, signify,
   speak for itself, speak volumes, stand by, subscribe to, suggest,
   support, sustain, swear and affirm, swear to, symptomatize,
   take kindly to, take up, tell, tend to show, think well of,
   tolerate, undersign, underwrite, uphold, validate, view with favor,
   visa, vise, vote affirmatively, vote aye, warrant, wink at,
   yield assent