The Collaborative International Dictionary of English v.0.48:

Happen \Hap"pen\ (h[a^]p"p'n), v. i. [imp. & p. p. Happened
   (-p'nd); p. pr. & vb. n. Happening.] [OE. happenen, hapnen.
   See Hap to happen.]
   1. To come by chance; to come without previous expectation;
      to fall out.
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            There shall no evil happen to the just. --Prov. xii.
                                                  21.
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   2. To take place; to occur.
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            All these things which had happened.  --Luke xxiv.
                                                  14.
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   To happen on, to meet with; to fall or light upon. "I have
      happened on some other accounts." --Graunt.

   To happen in, to make a casual call. [Colloq.]
      [1913 Webster]

WordNet (r) 3.0 (2006):

happen
    v 1: come to pass; "What is happening?"; "The meeting took place
         off without an incidence"; "Nothing occurred that seemed
         important" [syn: happen, hap, go on, pass off,
         occur, pass, fall out, come about, take place]
    2: happen, occur, or be the case in the course of events or by
       chance; "It happens that today is my birthday"; "These things
       befell" (Santayana) [syn: happen, befall, bechance]
    3: chance to be or do something, without intention or causation;
       "I happen to have just what you need!"
    4: come into being; become reality; "Her dream really
       materialized" [syn: happen, materialize, materialise]
       [ant: dematerialise, dematerialize]
    5: come upon, as if by accident; meet with; "We find this idea
       in Plato"; "I happened upon the most wonderful bakery not
       very far from here"; "She chanced upon an interesting book in
       the bookstore the other day" [syn: find, happen,
       chance, bump, encounter]

Moby Thesaurus II by Grady Ward, 1.0:

54 Moby Thesaurus words for "happen":
   be found, be met with, be realized, bechance, become of, befall,
   betide, break, bump, chance, come, come about, come along,
   come down, come off, come to pass, come true, come upon, cook,
   develop, do, encounter, eventuate, fall, fall out, find, give, go,
   go off, go on, hap, happen along, happen by chance, hazard, hit,
   light, luck, materialize, meet, meet with, occur, pass, pass off,
   pop up, prove, rise, stumble, stumble on, stumble upon, take place,
   transpire, tumble, turn out, turn up