The Collaborative International Dictionary of English v.0.48:

normality \nor*mal"i*ty\ n.
   1. Conformity with the norm; the state of being normal; the
      normal condition.

   Syn: normalcy.
        [WordNet 1.5]

WordNet (r) 3.0 (2006):

normality
    n 1: being within certain limits that define the range of normal
         functioning [syn: normality, normalcy] [ant:
         abnormalcy, abnormality]
    2: (of a solution) concentration expressed in gram equivalents
       of solute per liter [syn: normality, N]
    3: expectedness as a consequence of being usual or regular or
       common [syn: normality, normalcy]
    4: conformity with the norm

Moby Thesaurus II by Grady Ward, 1.0:

68 Moby Thesaurus words for "normality":
   appropriateness, averageness, balance, commonality, commonness,
   commonplaceness, contact with reality, conventionality,
   correctitude, correctness, currency, decencies, decency,
   decorousness, decorum, extensiveness, fitness, fittingness,
   garden variety, goodness, habitualness, healthy mind,
   lucid interval, lucidity, mental balance, mental equilibrium,
   mental health, mental hygiene, mental poise, niceness, normalcy,
   normalness, normativeness, ordinariness, prevalence, properness,
   proprieties, propriety, rampantness, rationality, reason,
   reasonableness, reign, rifeness, right mind, righteousness,
   rightness, routineness, run, sanemindedness, saneness, sanity,
   seemliness, senses, sober senses, sobriety, sound mind, soundness,
   soundness of mind, standardness, suitability, sweepingness,
   unexceptionality, unnoteworthiness, unremarkableness, usualness,
   wholesomeness, widespreadness