The Collaborative International Dictionary of English v.0.48:

Prevail \Pre*vail"\, v. i. [imp. & p. p. Prevailed; p. pr. &
   vb. n. Prevailing.] [F. pr['e]valoir, OF. prevaleir, L.
   praevalere; prae before + valere to be strong, able, or
   worth. See Valiant.]
   1. To overcome; to gain the victory or superiority; to gain
      the advantage; to have the upper hand, or the mastery; to
      succeed; -- sometimes with over or against.
      [1913 Webster]

            When Moses held up his hand, Israel prevailed, and
            when he let down his hand, Amalek prevailed. --Ex.
                                                  xvii. 11.
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            So David prevailed over the Philistine. --1 Sam.
                                                  xvii. 50.
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            This kingdom could never prevail against the united
            power of England.                     --Swift.
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   2. To be in force; to have effect, power, or influence; to be
      predominant; to have currency or prevalence; to obtain;
      as, the practice prevails this day.
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            This custom makes the short-sighted bigots, and the
            warier skeptics, as far as it prevails. --Locke.
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   3. To persuade or induce; -- with on, upon, or with; as, I
      prevailedon him to wait.
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            He was prevailed with to restrain the Earl.
                                                  --Clarendon.
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            Prevail upon some judicious friend to be your
            constant hearer, and allow him the utmost freedom.
                                                  --Swift.
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WordNet (r) 3.0 (2006):

prevail
    v 1: be larger in number, quantity, power, status or importance;
         "Money reigns supreme here"; "Hispanics predominate in this
         neighborhood" [syn: predominate, dominate, rule,
         reign, prevail]
    2: be valid, applicable, or true; "This theory still holds"
       [syn: prevail, hold, obtain]
    3: continue to exist; "These stories die hard"; "The legend of
       Elvis endures" [syn: prevail, persist, die hard, run,
       endure]
    4: prove superior; "The champion prevailed, though it was a hard
       fight" [syn: prevail, triumph]
    5: use persuasion successfully; "He prevailed upon her to visit
       his parents"

Moby Thesaurus II by Grady Ward, 1.0:

146 Moby Thesaurus words for "prevail":
   abide, affect, argue into, be, be blooded, be extant, be found,
   be in, be in existence, be in force, be met with, be present,
   be successful, be the case, be the rage, be the rule, be the thing,
   be there, be victorious, beat, best, bestride, better, bide,
   break the record, breathe, bring around, bring round, cap,
   carry on, catch on, click, come off, connect, continue,
   continue the same, continue to be, convince, defeat time,
   defy time, dictate, dispose, dominate, domineer, drag along,
   drag on, draw, drone, dwell, endure, exceed, excel, exist, extend,
   farewell, get, go, go great guns, go off, go on, go one better,
   go over, go over big, go to town, graduate, happen to be,
   have being, have place, have the ascendancy, hold, hold on,
   hold out, hum, impress, improve on, incline, induce, influence,
   keep, keep on, last, last long, last out, live, live on,
   live through, maintain, make a hit, master, meet with success,
   obtain, occur, outweigh, overbalance, overbear, overcome, overpass,
   overtop, pass, perdure, perennate, perfect, persist, persuade,
   play first fiddle, predominate, preponderate, prompt, prosper,
   qualify, reign, remain, rule, rule the roost, run, run on,
   run through, stand, stay, stay on, subsist, succeed, surpass,
   survive, sustain, sway, take, take the lead, talk into, tarry,
   tide over, top, tower above, tower over, transcend, triumph, trump,
   twist, wear, wear the pants, wear well, win, win out, win over,
   work well, work wonders