The Collaborative International Dictionary of English v.0.48:

Continuous \Con*tin"u*ous\, a. [L. continuus, fr. continere to
   hold together. See Continent.]
   1. Without break, cessation, or interruption; without
      intervening space or time; uninterrupted; unbroken;
      continual; unceasing; constant; continued; protracted;
      extended; as, a continuous line of railroad; a continuous
      current of electricity.
      [1913 Webster]

            he can hear its continuous murmur.    --Longfellow.
      [1913 Webster]

   2. (Bot.) Not deviating or varying from uninformity; not
      interrupted; not joined or articulated.
      [1913 Webster]

   Continuous brake (Railroad), a brake which is attached to
      each car a train, and can be caused to operate in all the
      cars simultaneously from a point on any car or on the
      engine.

   Continuous impost. See Impost.

   Syn: Continuous, Continual.

   Usage: Continuous is the stronger word, and denotes that the
          continuity or union of parts is absolute and
          uninterrupted; as, a continuous sheet of ice; a
          continuous flow of water or of argument. So Daniel
          Webster speaks of "a continuous and unbroken strain of
          the martial airs of England." Continual, in most
          cases, marks a close and unbroken succession of
          things, rather than absolute continuity. Thus we speak
          of continual showers, implying a repetition with
          occasional interruptions; we speak of a person as
          liable to continual calls, or as subject to continual
          applications for aid, etc. See Constant.
          [1913 Webster]

WordNet (r) 3.0 (2006):

continuous
    adj 1: continuing in time or space without interruption; "a
           continuous rearrangement of electrons in the solar atoms
           results in the emission of light"- James Jeans; "a
           continuous bout of illness lasting six months"; "lived in
           continuous fear"; "a continuous row of warehouses"; "a
           continuous line has no gaps or breaks in it"; "moving
           midweek holidays to the nearest Monday or Friday allows
           uninterrupted work weeks" [syn: continuous,
           uninterrupted] [ant: discontinuous, noncontinuous]
    2: of a function or curve; extending without break or
       irregularity [ant: discontinuous]

Moby Thesaurus II by Grady Ward, 1.0:

133 Moby Thesaurus words for "continuous":
   abiding, accordant, ageless, alike, articulated, automatic,
   balanced, catenated, ceaseless, chronological, coeternal,
   concatenated, connected, consecutive, consistent, consonant,
   constant, continual, continued, continuing, correspondent,
   cyclical, dateless, direct, durational, durative, endless, equable,
   equal, eternal, eterne, even, ever-being, ever-durable,
   ever-during, ever-recurring, everlasting, everliving, featureless,
   flat, frequent, gapless, haunting, homogeneous, immediate,
   immemorial, immutable, incessant, indefatigable, indestructible,
   infinite, interminable, invariable, joined, jointless, lasting,
   level, linked, measured, mechanical, methodic, monolithic,
   monotonous, never-ceasing, never-ending, nonstop, nonterminating,
   nonterminous, of a piece, olamic, ordered, orderly, perdurable,
   perennial, periodic, permanent, perpetual, persistent, reappearing,
   recurrent, recurring, regular, remaining, repetitive, returning,
   revenant, robotlike, round-the-clock, running, seamless,
   sempiternal, sequent, sequential, serial, serried, smooth, stable,
   staying, steadfast, steady, sticking, straight, sustained,
   systematic, temporal, thematic, thick-coming, tight, timeless,
   twenty-four-hour, ubiquitous, unbroken, unceasing, unchangeable,
   unchanged, unchanging, undeviating, undifferentiated,
   undiversified, undying, unending, uniform, unintermitted,
   unintermittent, unintermitting, uninterrupted, unrelieved,
   unremitting, unruffled, unstopped, unvaried, unvarying,
   without end