The Collaborative International Dictionary of English v.0.48:

Babble \Bab"ble\ (b[a^]b"b'l), v. i. [imp. & p. p. Babbled
   (b[a^]b"b'ld); p. pr. & vb. n. Babbling.] [Cf. LG. babbeln,
   D. babbelen, G. bappeln, bappern, F. babiller, It. babbolare;
   prob. orig., to keep saying ba, imitative of a child learning
   to talk.]
   1. To utter words indistinctly or unintelligibly; to utter
      inarticulate sounds; as a child babbles.
      [1913 Webster]

   2. To talk incoherently; to utter unmeaning words.
      [1913 Webster]

   3. To talk much; to chatter; to prate.
      [1913 Webster]

   4. To make a continuous murmuring noise, as shallow water
      running over stones.
      [1913 Webster]

            In every babbling brook he finds a friend.
                                                  --Wordsworth.
      [1913 Webster]

   Note: Hounds are said to babble, or to be babbling, when they
         are too noisy after having found a good scent.
         [1913 Webster]

   Syn: To prate; prattle; chatter; gossip.
        [1913 Webster]

WordNet (r) 3.0 (2006):

babbling
    n 1: gibberish resembling the sounds of a baby [syn: babble,
         babbling, lallation]

Moby Thesaurus II by Grady Ward, 1.0:

51 Moby Thesaurus words for "babbling":
   arrested, backward, blithering, bubbling, burbling, crackbrained,
   cracked, crazy, cretinistic, cretinous, delirious, dithering,
   dizzy, driveling, drooling, giddy, guggling, gurgling, half-baked,
   half-witted, idiotic, imbecile, imbecilic, incoherent, lapping,
   lightheaded, maundering, mentally defective, mentally deficient,
   mentally handicapped, mentally retarded, mongoloid, moronic,
   not all there, off, plashing, rambling, ranting, raving, retarded,
   rippling, simple, simpleminded, simpletonian, slobbering, sloshing,
   splashing, subnormal, swishing, trilling, wandering