In school, we learn the conjugations of "haben", but "hab" is not one of them. When is "hab" used and is it colloqial?
The form »hab« in fact is an official conjugation of the verb »haben« in standard German. It is one of the two possible versions of the imperative singular (see »haben« in Wiktionary, watch the box on the right). You can use it in sentences like
Habe Angst! = Hab Angst!
Be afraid! (verbatim: Have fear!)
But the most frequent usage is a command that soldiers might hear from their drill sergeants:
Attention! (verbatime: Have respect!; »Acht« = old variation of »Achtung« which can mean attention as well as respect)
This singular version also very often is used if more than one soldier is drilled, but of course there also exists the plural version, which is »Habt Acht!«
But there also is a second usage for »hab«, which is not an imperative, but a colloquial (i.e. non-standard) form of the verb in present tense, singular for the 1st person:
Standard: Ich habe dich lieb. - Colloquial: Ich hab dich lieb.
The meaning is in the middle between "I like you" and "I love you". For more details consult the question What’s the difference between “Ich habe dich lieb” and “Ich liebe dich”?.
Since colloquial language almost exclusively exists in spoken language, you hardly will find the colloquial indicative hab in written texts. If it is used in written texts, the omitted e often (but not always) is indicated by an apostrophe:
Ich hab’ dich lieb.
Yes, its colloquial and heavily dependent on the region. Hab is a sloppy form of
with the trailing e omitted. In writing this is seldom done, and in the rare cases an apostrophe is written instead of the e.
For the imperative singular the form hab is perfectly legal in addition to habe (see [Wiktionary])1, so the e never harms.