The Collaborative International Dictionary of English v.0.48:

Involve \In*volve"\, v. t. [imp. & p. p. Involved; p. pr. &
   vb. n. Involving.] [L. involvere, involutum, to roll about,
   wrap up; pref. in- in + volvere to roll: cf. OF. involver.
   See Voluble, and cf. Involute.]
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   1. To roll or fold up; to wind round; to entwine.
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            Some of serpent kind . . . involved
            Their snaky folds.                    --Milton.
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   2. To envelop completely; to surround; to cover; to hide; to
      involve in darkness or obscurity.
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            And leave a sing[`e]d bottom all involved
            With stench and smoke.                --Milton.
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   3. To complicate or make intricate, as in grammatical
      structure. "Involved discourses." --Locke.
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   4. To connect with something as a natural or logical
      consequence or effect; to include necessarily; to imply.
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            He knows
            His end with mine involved.           --Milton.
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            The contrary necessarily involves a contradiction.
                                                  --Tillotson.
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   5. To take in; to gather in; to mingle confusedly; to blend
      or merge. [R.]
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            The gathering number, as it moves along,
            Involves a vast involuntary throng.   --Pope.
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            Earth with hell
            To mingle and involve.                --Milton.
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   6. To envelop, infold, entangle, or embarrass; as, to involve
      a person in debt or misery.
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   7. To engage thoroughly; to occupy, employ, or absorb.
      "Involved in a deep study." --Sir W. Scott.
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   8. (Math.) To raise to any assigned power; to multiply, as a
      quantity, into itself a given number of times; as, a
      quantity involved to the third or fourth power.

   Syn: To imply; include; implicate; complicate; entangle;
        embarrass; overwhelm.

   Usage: To Involve, Imply. Imply is opposed to express, or
          set forth; thus, an implied engagement is one fairly
          to be understood from the words used or the
          circumstances of the case, though not set forth in
          form. Involve goes beyond the mere interpretation of
          things into their necessary relations; and hence, if
          one thing involves another, it so contains it that the
          two must go together by an indissoluble connection.
          War, for example, involves wide spread misery and
          death; the premises of a syllogism involve the
          conclusion.
          [1913 Webster]

WordNet (r) 3.0 (2006):

involve
    v 1: connect closely and often incriminatingly; "This new ruling
         affects your business" [syn: involve, affect, regard]
    2: engage as a participant; "Don't involve me in your family
       affairs!"
    3: have as a necessary feature; "This decision involves many
       changes" [syn: imply, involve]
    4: require as useful, just, or proper; "It takes nerve to do
       what she did"; "success usually requires hard work"; "This
       job asks a lot of patience and skill"; "This position demands
       a lot of personal sacrifice"; "This dinner calls for a
       spectacular dessert"; "This intervention does not postulate a
       patient's consent" [syn: necessitate, ask, postulate,
       need, require, take, involve, call for, demand]
       [ant: eliminate, obviate, rid of]
    5: contain as a part; "Dinner at Joe's always involves at least
       six courses"
    6: occupy or engage the interest of; "His story completely
       involved me during the entire afternoon"
    7: make complex or intricate or complicated; "The situation was
       rather involved"

Moby Thesaurus II by Grady Ward, 1.0:

256 Moby Thesaurus words for "involve":
   absorb, absorb the attention, adorn, affect, affect the interest,
   allegorize, allude to, answer to, appertain to, apply to, approve,
   argue, arrest, assail, associate with, assume, attack, attest,
   attract, ball up, be indicative of, be significant of,
   be symptomatic of, bear on, bear upon, belong to, bespeak, betoken,
   breathe, bring, bring to mind, burden, call for, catch, catch up,
   catch up in, censure, characterize, charm, close, compass,
   compass about, complicate, comprehend, comprise, concern, confound,
   confuse, connect, connect with, connote, contain, convolute,
   correspond to, count in, cover, cramp, criminate, cripple,
   cry out against, cry out on, cry shame upon, cumber, deal with,
   decorate, demonstrate, denominate, denote, differentiate, disclose,
   display, draw in, elaborate, embarrass, embay, embellish, embody,
   embosom, embrace, embrangle, embroider, embroil, enchant, enclasp,
   enclose, encompass, encumber, enfold, engage, engage the attention,
   engage the mind, engage the thoughts, engross, engross the mind,
   engross the thoughts, enmesh, enrich, ensnarl, entail, entangle,
   enthrall, entoil, entrammel, entrap, entwine, envelop, environ,
   enwrap, evidence, evince, excite, excite interest, exercise,
   exhibit, express, fascinate, festoon, fetter, flourish, foul up,
   furnish evidence, gild, give evidence, give indication of,
   give token, go around, go round, go to show, grab, grip, hamper,
   hamstring, handicap, have, have connection with, highlight, hint,
   hobble, hold, hold spellbound, hold the interest, hypnotize,
   identify, illustrate, immerse, impede, implicate, imply, import,
   impugn, include, incorporate, incriminate, inculpate, indicate,
   infer, insinuate, interest, intimate, invest, invite, involve in,
   involve the interest, knot, lame, lap, lead to, liaise with, lime,
   link with, load with ornament, louse up, lumber, manifest, mark,
   mean, mean to say, mesmerize, mess up, mire, mix up, monopolize,
   muck up, muddle, necessitate, net, note, number among, obsess,
   occupy, occupy the attention, ornament, overcharge, overlay,
   overload, perplex, pertain to, pique, point indirectly to,
   point to, preoccupy, press down, presume, presuppose, provoke,
   ramify, ravel, refer to, regard, relate to, require, respect,
   reveal, saddle with, screw up, set forth, shackle, show,
   show signs of, signalize, signify, snarl, snarl up,
   speak for itself, speak volumes, spellbind, stand for, stimulate,
   subsume, suck into, suggest, suppose, surround, symptomatize,
   symptomize, take, take for granted, take in, take up, tangle,
   tantalize, tell, tend to show, testify, tickle, tie in with,
   titillate, toil, touch, touch upon, trammel, treat of, trick out,
   varnish, weigh down, wrap