The Collaborative International Dictionary of English v.0.48:

Rival \Ri"val\, v. t. [imp. & p. p. Rivaledor Rivalled; p.
   pr. & vb. n. Rivaling or Rivalling.]
   1. To stand in competition with; to strive to gain some
      object in opposition to; as, to rival one in love.
      [1913 Webster]

   2. To strive to equal or exel; to emulate.
      [1913 Webster]

            To rival thunder in its rapid course. --Dryden.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Rival \Ri"val\, v. i.
   To be in rivalry. [Obs.] --Shak.
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Rival \Ri"val\, a.
   Having the same pretensions or claims; standing in
   competition for superiority; as, rival lovers; rival claims
   or pretensions.
   [1913 Webster]

         The strenuous conflicts and alternate victories of two
         rival confederacies of statesmen.        --Macaulay.
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The Collaborative International Dictionary of English v.0.48:

Rival \Ri"val\, n. [F. rival (cf. It. rivale), L. rivales two
   neigbors having the same brook in common, rivals, fr. rivalis
   belonging to a brook, fr. rivus a brook. Cf. Rivulet,
   Rete.]
   1. A person having a common right or privilege with another;
      a partner. [Obs.]
      [1913 Webster]

            If you do meet Horatio and Marcellus,
            The rivals of my watch, bid them make haste. --Shak.
      [1913 Webster]

   2. One who is in pursuit of the same object as another; one
      striving to reach or obtain something which another is
      attempting to obtain, and which one only can posses; a
      competitor; as, rivals in love; rivals for a crown.
      [1913 Webster]

   Note: "Rivals, in the primary sense of the word, are those
         who dwell on the banks of the same stream. But since,
         as all experience shows, there is no such fruitful
         source of coutention as a water right, it would
         continually happen that these occupants of the opposite
         banks would be at strife with one another in regard of
         the periods during which they severally had a right to
         the use of the stream . . . And thus 'rivals' . . .
         came to be used of any who were on any grounds in more
         or less unfriendly competition with one another."
         --Trench.
         [1913 Webster]

   Syn: Competitor; emulator; antagonist.
        [1913 Webster]

WordNet (r) 3.0 (2006):

rival
    n 1: the contestant you hope to defeat; "he had respect for his
         rivals"; "he wanted to know what the competition was doing"
         [syn: rival, challenger, competitor, competition,
         contender]
    v 1: be equal to in quality or ability; "Nothing can rival
         cotton for durability"; "Your performance doesn't even
         touch that of your colleagues"; "Her persistence and
         ambition only matches that of her parents" [syn: equal,
         touch, rival, match]
    2: be the rival of, be in competition with; "we are rivaling for
       first place in the race"

Moby Thesaurus II by Grady Ward, 1.0:

203 Moby Thesaurus words for "rival":
   admit of comparison, adversary, adversative, adverse, alien,
   amount to, antagonist, antagonistic, antagonize, anti,
   antipathetic, antithetic, approach, attempt, balance, battle,
   battler, be commensurable, be comparable, beat against,
   beat up against, belligerent, belted knight, bickerer, blade,
   bravo, brawler, break even, breast the wave, buck, buffet,
   buffet the waves, bully, bullyboy, challenge, challenge comparison,
   clashing, close with, coequal, combat, combatant, come to,
   come up to, compare, compare to, compare with, compeer, compete,
   compete with, competing, competition, competitive, competitor, con,
   conflicting, contend, contend against, contend with, contender,
   contest, contestant, contradictory, contrary, cope, correspond,
   correspond to, corrival, counter, counterpart, cross, cutthroat,
   disaccordant, disputant, dissentient, ditto, draw, duelist,
   emulate, emulator, emulous, enemy, enforcer, entrant, equal,
   equipollent, equivalent, even, even off, fellow, fencer, feuder,
   fight, fight against, fighter, fighting cock, foilsman, fractious,
   gamecock, gladiator, goon, gorilla, grapple with, hatchet man,
   hood, hoodlum, hooligan, hostile, in competition, in rivalry,
   inimical, jockey, join battle with, jouster, keep pace with,
   knight, knot, labor against, like, match, match up with, mate,
   measure up, measure up to, meet, militant, militate against,
   negative, noncooperative, not compare with, obstinate,
   offer resistance, opponent, oppose, opposed, opposing, opposite,
   opposite number, opposition, oppositional, oppositive, oppugnant,
   outvie, overthwart, parallel, partake of, peer, perverse, player,
   plug-ugly, quarreler, reach, recalcitrant, refractory, reluct,
   reluctate, repugnant, resemble, rioter, rivaling, rough, rowdy,
   ruffian, run abreast, run to, sabreur, scrapper, scuffler,
   squabbler, stack up with, stem the tide, strive, strive against,
   strong arm, strong-arm man, strong-armer, struggle,
   struggle against, struggle with, struggler, swashbuckler, sword,
   swordplayer, swordsman, take on, test one another, the field, thug,
   tie, tilter, touch, tough, try, tussler, twin, uncooperative,
   unfavorable, unfriendly, unpropitious, vie, vie with, vier, vying,
   wrangler