carven,
"I haven't" is and older form with the same meaning as "I don't have". It is not a short form for
"I haven't got" which is another way to express possession.
"I haven't" seems old-fashioned to some but (in Canada) you still hear it:
-I haven't a clue.
-I haven't a penny to my name.
-I haven't the time to explain all that to you.
-I haven't any reason to be mad.
-I may be willing to travel, but I haven't a passport yet.
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-I haven't a particle of confidence in a man who has no redeeming petty vices. - (Mark Twain, American writer)
-I haven't any right to criticize books, and I don't do it except when I hate them. I often want to criticize Jane Austen, but her books madden me so that I can't conceal my frenzy from the reader; and therefore I have to stop every time I begin. Every time I read Pride and Prejudice I want to dig her up and beat her over the skull with her own shin-bone.-- Mark Twain 1898
The full form --I have not-- is rarely used in speech. You might find it in formal writing or used for emphasis as Genco stated above.