Writing
"Ich habe" is the accepted correct written form. It is always OK to use it.
It is never OK to use "ich hab" in professional or official written communication.
"Ich hab" is fine in informal conversations like forums, chat rooms or personal E-Mails.
However, even if the spoken form would be thick with colloquialisms, it is perfectly normal for informal written communication to obey the rules of correct German.
Real world example: When I speak with my father, we use very heavy swabian. In all written communication however, we use perfect high german.
Speaking
In speaking, "Ich habe" is never wrong. However, in most everyday informal conversations in most areas of the country, the trailing e is swallowed.
To someone learning German as a second language, I'd say if in doubt, use "ich habe". Continued exposure to everyday interactions with Germans will show you quickly when and where it is usually dropped.
Ich habis perfectly ok in professional communication: "Ich hab keine Äpfel mehr" sagte dei Marktfrau. "Ich hab den auch in Rot", sagte der Autohändler. "Ich hab selbst ein Glasauge" sagte der Optiker. "Ich hab das Bailout für Griechenland fertig" sagte der Minister zur Kanzlerin. Ich seh da kein Problem. Even the apostroph is dropped, so common is the usage. – user unknown Jun 06 '11 at 16:25dafür soll' sich das Land an den Kosten beteiligen. A few minutes later: "Lybien soll sich..." and "deshalb wär' die Chance groß gewesen den Erreger zu finden". In the communication of politics or economic organisations, first person singular language is generally rare. Most spokesmen say either "we" or use passive language "it has been shown". Apostrophs only used, to indicate, where theeis missing. – user unknown Jun 06 '11 at 18:32It is never OK to use "ich hab" in professional or official communicationis related to writing. Show me an instance where the abbreviated form is used in a written, official document – Pekka Jun 06 '11 at 18:43'?) Am I blind? – Hendrik Vogt Jun 06 '11 at 21:25elike inseh, geh, steh, hab, but a lostetoo -er solle dies und jenes - er soll' dies und jenes. – user unknown Jun 07 '11 at 13:45