The Collaborative International Dictionary of English v.0.48:

Rigorous \Rig"or*ous\, a. [F. rigoureux, LL. rigorosus. See
   Rigor.]
   1. Manifesting, exercising, or favoring rigor; allowing no
      abatement or mitigation; scrupulously accurate; exact;
      strict; severe; relentless; as, a rigorous officer of
      justice; a rigorous execution of law; a rigorous
      definition or demonstration.
      [1913 Webster]

            He shall be thrown down the Tarpeian Rock
            With rigorous hands.                  --Shak.
      [1913 Webster]

            We do not connect the scattered phenomena into their
            rigorous unity.                       --De Quincey.
      [1913 Webster]

   2. Severe; intense; inclement; as, a rigorous winter.
      [1913 Webster]

   3. Violent. [Obs.] "Rigorous uproar." --Spenser.
      [1913 Webster]

   4. (Mathematics, Logic) Adhering scrupulously and exactly to
      accepted principles; hence, logically valid; as, a
      rigorous proof.
      [PJC]

   Syn: Rigid; inflexible; unyielding; stiff; severe; austere;
        stern; harsh; strict; exact.
        [1913 Webster] -- Rig"or*ous*ly, adv. --
        Rig"or*ous*ness, n.
        [1913 Webster]

WordNet (r) 3.0 (2006):

rigorous
    adj 1: rigidly accurate; allowing no deviation from a standard;
           "rigorous application of the law"; "a strict vegetarian"
           [syn: rigorous, strict]
    2: demanding strict attention to rules and procedures; "rigorous
       discipline"; "tight security"; "stringent safety measures"
       [syn: rigorous, stringent, tight]

Moby Thesaurus II by Grady Ward, 1.0:

261 Moby Thesaurus words for "rigorous":
   Herculean, Siberian, abstruse, accurate, acid, acidulous, acrid,
   acrimonious, acute, adamant, adamantine, adverse, algid,
   antagonistic, arctic, arduous, ascetic, astringent, attentive,
   below zero, biting, bitter, bitterly cold, bleak, boreal, brisk,
   brumal, brutal, burdensome, cast-iron, caustic, close, cold,
   cold as charity, cold as death, cold as ice, cold as marble,
   complex, conflicting, conscientious, constant, contrary, correct,
   counter, counteractive, crisp, critical, cutting, delicate,
   demanding, detailed, detrimental, difficile, difficult, direct,
   double-edged, dour, draconian, drastic, edged, escharotic, even,
   exact, exacting, excessive, exigent, exorbitant, express,
   exquisite, extravagant, extreme, faithful, fierce, fine, finical,
   finicking, finicky, firm, flinty, formidable, freezing,
   freezing cold, frigid, fundamentalist, furious, fussy, gelid,
   glacial, great, grim, hairy, hard, hard-core, hard-earned,
   hard-fought, harmful, harsh, hibernal, hidebound, hiemal, hostile,
   hyperborean, ice-cold, ice-encrusted, icelike, icy, immoderate,
   immovable, immutable, implacable, impliable, in opposition,
   incisive, inclement, inelastic, inerrable, inerrant, inexorable,
   infallible, inflexible, inimical, intemperate, intense,
   intransigent, intricate, iron, ironbound, ironclad, ironhanded,
   irreconcilable, jawbreaking, keen, knotted, knotty, laborious,
   mathematical, mean, meticulous, micrometrically precise,
   microscopic, minute, miserable, mordacious, mordant, muscle-bound,
   narrow, nice, nipping, nippy, no picnic, not easy, numbing,
   obdurate, obstinate, onerous, operose, opposed, opposing, opposite,
   oppressive, orthodox, outrageous, particular, penetrating,
   piercing, pinching, pinpoint, poignant, precise, precisianistic,
   precisionistic, procrustean, proper, punctilious, punctual, purist,
   puristic, puritan, puritanic, raw, refined, relentless, religious,
   religiously exact, right, rigid, rigorist, rigoristic, rock-ribbed,
   rockbound, rough, rugged, scathing, scientific,
   scientifically exact, scrupulous, scrutinizing, set with thorns,
   severe, sharp, sinister, sleety, slushy, snappy, spiny, splitting,
   square, stabbing, steely, steep, stern, stiff, stinging,
   stone-cold, straightlaced, straitlaced, strenuous, stressful,
   strict, strident, stringent, stubborn, subtle, subzero,
   supercooled, tart, thorny, ticklish, toilsome, tough, trenchant,
   tricky, troublesome, troublous, trying, unaffected, unalterable,
   unbending, unchangeable, uncompromising, unconscionable,
   undeviating, unerring, unfavorable, ungiving, unmoved, unrelenting,
   untoward, unyielding, uphill, vehement, venomous, violent,
   virulent, vitriolic, wicked, winterbound, winterlike, wintery,
   wintry, wretched