The Collaborative International Dictionary of English v.0.48:

Consecutive \Con*sec"u*tive\, a. [Cf. F. cons['e]cutif. See
   Consequent.]
   1. Following in a train; succeeding one another in a regular
      order; successive; uninterrupted in course or succession;
      with no interval or break; as, fifty consecutive years.
      [1913 Webster]

   2. Following as a consequence or result; actually or
      logically dependent; consequential; succeeding.
      [1913 Webster]

            The actions of a man consecutive to volition.
                                                  --Locke.
      [1913 Webster]

   3. (Mus.) Having similarity of sequence; -- said of certain
      parallel progressions of two parts in a piece of harmony;
      as, consecutive fifths, or consecutive octaves, which are
      forbidden.
      [1913 Webster]

   Consecutive chords (Mus.), chords of the same kind
      succeeding one another without interruption.
      [1913 Webster]

WordNet (r) 3.0 (2006):

consecutive
    adv 1: in a consecutive manner; "we numbered the papers
           consecutively" [syn: consecutive, sequentially]
    adj 1: one after the other; "back-to-back home runs" [syn:
           back-to-back, consecutive]
    2: in regular succession without gaps; "serial concerts" [syn:
       consecutive, sequent, sequential, serial,
       successive]
    3: successive (without a break); "sick for five straight days"
       [syn: straight, consecutive]

Moby Thesaurus II by Grady Ward, 1.0:

33 Moby Thesaurus words for "consecutive":
   after, attendant, cadet, catenary, connected, consistent,
   continuous, enlarging, ensuing, following, increasing, joined,
   junior, later, lineal, linear, orderly, ordinal, posterior,
   progressive, puisne, sequent, sequential, serial, seriate,
   subsequent, succeeding, successional, successive, tight, trailing,
   uninterrupted, younger