VERB (3)

1. be obliged to pay or repay;

2. be indebted to, in an abstract or intellectual sense;
- Example: "This new theory owes much to Einstein's Relativity Theory"

3. be in debt;
- Example: "She owes me $200"
- Example: "I still owe for the car"
- Example: "The thesis owes much to his adviser"

The Collaborative International Dictionary of English v.0.48:

Owe \Owe\ ([=o]), v. t. [imp. & p. p. Owed ([=o]d), (Ought
   ([add]t) obs.); p. pr. & vb. n. Owing ([=o]"[i^]ng).] [OE.
   owen, awen, aghen, to have, own, have (to do), hence, owe,
   AS. [=a]gan to have; akin to G. eigen, a., own, Icel. eiga to
   have, Dan. eie, Sw. [aum]ga, Goth. ['a]igan, Skr. [imac][,c].
   [root]110. Cf. Ought, v., 2d Own, Fraught.]
   1. To possess; to have, as the rightful owner; to own. [Obs.]
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            Thou dost here usurp
            The name thou ow'st not.              --Shak.
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   2. To have or possess, as something derived or bestowed; to
      be obliged to ascribe (something to some source); to be
      indebted or obliged for; as, he owed his wealth to his
      father; he owed his victory to his lieutenants. --Milton.
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            O deem thy fall not owed to man's decree. --Pope.
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   3. Hence: To have or be under an obigation to restore, pay,
      or render (something) in return or compensation for
      something received; to be indebted in the sum of; as, the
      subject owes allegiance; the fortunate owe assistance to
      the unfortunate.
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            The one ought five hundred pence, and the other
            fifty.                                --Bible
                                                  (1551).
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            A son owes help and honor to his father. --Holyday.
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   Note: Owe was sometimes followed by an objective clause
         introduced by the infinitive. "Ye owen to incline and
         bow your heart." --Chaucer.
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   4. To have an obligation to (some one) on account of
      something done or received; to be indebted to; as, to owe
      the grocer for supplies, or a laborer for services.
      [1913 Webster]

WordNet (r) 3.0 (2006):

owe
    v 1: be obliged to pay or repay
    2: be indebted to, in an abstract or intellectual sense; "This
       new theory owes much to Einstein's Relativity Theory"
    3: be in debt; "She owes me $200"; "I still owe for the car";
       "The thesis owes much to his adviser"

The Devil's Dictionary (1881-1906):

OWE, v.  To have (and to hold) a debt.  The word formerly signified
not indebtedness, but possession; it meant "own," and in the minds of
debtors there is still a good deal of confusion between assets and
liabilities.