The Collaborative International Dictionary of English v.0.48:

Responsible \Re*spon"si*ble\ (r?*sp?n"s?*b'l), a. [Cf. F.
   responsable. See Respond.]
   1. Liable to respond; likely to be called upon to answer;
      accountable; answerable; amenable; as, a guardian is
      responsible to the court for his conduct in the office.
      [1913 Webster]

   2. Able to respond or answer for one's conduct and
      obligations; trustworthy, financially or otherwise; as, to
      have a responsible man for surety.
      [1913 Webster]

   3. Involving responsibility; involving a degree of
      accountability on the part of the person concerned; as, a
      responsible office.
      [1913 Webster]

   Syn: Accountable; answerable; amenable.
        [1913 Webster] -- Re*spon"si*ble*ness, n. --
        Re*spon"si*bly, adv.
        [1913 Webster]

WordNet (r) 3.0 (2006):

responsibleness
    n 1: a form of trustworthiness; the trait of being answerable to
         someone for something or being responsible for one's
         conduct; "he holds a position of great responsibility"
         [syn: responsibility, responsibleness] [ant:
         irresponsibility, irresponsibleness]