The Collaborative International Dictionary of English v.0.48:

Universality \U`ni*ver*sal"i*ty\, n.; pl. Universalties. [Cf.
   F. universalit['e].]
   The quality or state of being universal; unlimited extension
   or application; generality; -- distinguished from
   particularity; as, the unversality of a proposition; the
   unversality of sin; the unversality of the Deluge.
   [1913 Webster]

WordNet (r) 3.0 (2006):

universality
    n 1: the quality of being universal; existing everywhere [syn:
         universality, catholicity]

Moby Thesaurus II by Grady Ward, 1.0:

57 Moby Thesaurus words for "universality":
   all-comprehensiveness, all-inclusiveness, boundlessness,
   catholicity, completeness, comprehensiveness, cosmopolitanism,
   countlessness, ecumenicalism, ecumenicity, endlessness, entireness,
   entirety, eternity, exhaustiveness, exhaustlessness, forever,
   fullness, generality, generalization, globalism, globality, holism,
   illimitability, immeasurability, immensity, incalculability,
   inclusiveness, incomprehensibility, inexhaustibility, infiniteness,
   infinitude, infinity, innumerability, intactness, integrality,
   integrity, interminability, internationalism, limitlessness,
   measurelessness, numberlessness, omnipresence, perpetuity,
   pervasiveness, solidarity, solidity, termlessness, thoroughness,
   total approach, totality, ubiquity, unity, unmeasurability,
   wholeness, world without end, worldwideness