The Collaborative International Dictionary of English v.0.48:

Believe \Be*lieve"\, v. t. [imp. & p. p. Believed; p. pr. &
   vb. n. Believing.] [OE. bileven (with pref. be- for AS.
   ge-), fr. AS. gel?fan, gel?fan; akin to D. gelooven, OHG.
   gilouban, G. glauben, OS. gil?bian, Goth. galaubjan, and
   Goth. liubs dear. See Lief, a., Leave, n.]
   To exercise belief in; to credit upon the authority or
   testimony of another; to be persuaded of the truth of, upon
   evidence furnished by reasons, arguments, and deductions of
   the mind, or by circumstances other than personal knowledge;
   to regard or accept as true; to place confidence in; to
   think; to consider; as, to believe a person, a statement, or
   a doctrine.
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         Our conqueror (whom I now
         Of force believe almighty).              --Milton.
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         King Agrippa, believest thou the prophets ? --Acts
                                                  xxvi. 27.
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         Often followed by a dependent clause.
         I believe that Jesus Christ is the Son of God. --Acts
                                                  viii. 37.
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   Syn: See Expect.
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The Collaborative International Dictionary of English v.0.48:

Believe \Be*lieve"\, v. i.
   1. To have a firm persuasion, esp. of the truths of religion;
      to have a persuasion approaching to certainty; to exercise
      belief or faith.
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            Lord, I believe; help thou mine unbelief. --Mark ix.
                                                  24.
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            With the heart man believeth unto righteousness.
                                                  --Rom. x. 10.
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   2. To think; to suppose.
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            I will not believe so meanly of you.  --Fielding.
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   To believe in.
      (a) To believe that the subject of the thought (if a
          person or thing) exists, or (if an event) that it has
          occurred, or will occur; -- as, to believe in the
          resurrection of the dead. "She does not believe in
          Jupiter." --J. H. Newman.
      (b) To believe that the character, abilities, and purposes
          of a person are worthy of entire confidence; --
          especially that his promises are wholly trustworthy.
          "Let not your heart be troubled: ye believe in God,
          believe also in me." --John xiv. 1.
      (c) To believe that the qualities or effects of an action
          or state are beneficial: as, to believe in sea
          bathing, or in abstinence from alcoholic beverages.

   To believe on, to accept implicitly as an object of
      religious trust or obedience; to have faith in.
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WordNet (r) 3.0 (2006):

believe
    v 1: accept as true; take to be true; "I believed his report";
         "We didn't believe his stories from the War"; "She believes
         in spirits" [ant: disbelieve, discredit]
    2: judge or regard; look upon; judge; "I think he is very
       smart"; "I believe her to be very smart"; "I think that he is
       her boyfriend"; "The racist conceives such people to be
       inferior" [syn: think, believe, consider, conceive]
    3: be confident about something; "I believe that he will come
       back from the war" [syn: believe, trust]
    4: follow a credo; have a faith; be a believer; "When you hear
       his sermons, you will be able to believe, too"
    5: credit with veracity; "You cannot believe this man"; "Should
       we believe a publication like the National Enquirer?"

Moby Thesaurus II by Grady Ward, 1.0:

86 Moby Thesaurus words for "believe":
   accept, accept for gospel, accept implicitly, accredit, admit,
   allow, assume, be afraid, be certain, be pious, be religious,
   believe in, believe without reservation, buy, conceive, conclude,
   confide in, conjecture, consider, credit, daresay, deduce, deem,
   divine, dream, expect, fancy, fear God, feel, gather,
   give faith to, grant, have confidence in, have faith,
   have faith in, hold, hope in, imagine, infer, keep the faith, let,
   let be, love God, maintain, make believe, opine,
   place confidence in, place reliance in, prefigure, presume,
   presuppose, presurmise, pretend, provisionally accept,
   put faith in, put trust in, receive, reckon, rely on, rely upon,
   repose confidence in, repose in, repute, rest in, say, sense,
   set store by, suppose, surmise, suspect, swallow, swear by, take,
   take for, take for granted, take it, take on faith, take on trust,
   take stock in, take to be, think, trust, trust in, trust in God,
   trust to, understand