The Collaborative International Dictionary of English v.0.48:

Neediness \Need"i*ness\ (n[=e]d"[i^]*n[e^]s), n.
   The state or quality of being needy; want; poverty;
   indigence.
   [1913 Webster]

WordNet (r) 3.0 (2006):

neediness
    n 1: a state of extreme poverty [syn: privation, want,
         deprivation, neediness]
    2: the quality of needing attention and affection and
       reassurance to a marked degree; "he recognized her neediness
       but had no time to respond to it"