The Collaborative International Dictionary of English v.0.48:

Unbounded \Un*bound"ed\, a.
   Having no bound or limit; as, unbounded space; an, unbounded
   ambition. --Addison. -- Un*bound"ed*ly, adv. --
   Un*bound"ed*ness, n.
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Unbounded \Unbounded\
   See bounded.

WordNet (r) 3.0 (2006):

unbounded
    adj 1: seemingly boundless in amount, number, degree, or
           especially extent; "unbounded enthusiasm"; "children with
           boundless energy"; "a limitless supply of money" [syn:
           boundless, unbounded, limitless]

Moby Thesaurus II by Grady Ward, 1.0:

95 Moby Thesaurus words for "unbounded":
   absolute, all-comprehensive, all-inclusive, all-knowing,
   all-powerful, all-seeing, all-wise, almighty, boundless,
   changeless, countless, creating, creative, endless, eternal,
   eternally the same, everlasting, exhaustless, extending everywhere,
   full, glorious, good, hallowed, highest, holy, illimitable,
   illimited, immeasurable, immense, immortal, immutable,
   incalculable, incomprehensible, indefinite, inexhaustible,
   infinite, infinitely continuous, innumerable, interminable,
   interminate, just, limitless, loving, luminous, majestic, making,
   measureless, merciful, no end of, no strings, numinous, omnipotent,
   omnipresent, omniscient, one, open, perfect, permanent, perpetual,
   plenary, radiant, sacred, shaping, shoreless, sovereign, sumless,
   supreme, termless, timeless, ubiquitous, unbound, unchanging,
   uncircumscribed, unconditional, unconditioned, unconfined,
   undefined, unequivocal, unfathomable, universal, unlimited,
   unmeasurable, unmeasured, unnumbered, unplumbed, unqualified,
   unrestricted, untold, wide-open, without bound, without end,
   without limit, without measure, without number, without strings