It definitely isn't rare, and it definitely isn't found only in poetry. Any good Latin grammar will address this topic.
In Gildersleeve and Lodge, Latin grammar, the index entry for esse includes a subentry for 'omitted.' The main section where this topic is treated is 209. It gives a general rule, examples, and then notes, including a note that addresses omission of verbs other than esse.
209. COPULA OMITTED.—Est or sunt is often omitted in saws and proverbs, in short statements and questions, in rapid changes, in conditional clauses, and in tenses compounded with participles:
Summum iūs summa iniūria, C., Off., I. 10, 33; the height of right (is) the height of wrong. Nēmo malus fēlix, Juv., IV. 8; no bad man (is) happy. Quid dulcius quam habēre quīcum omnia audeās loquī? C. Lael., 7, 22; what sweeter than to have some one with whom you can venture to talk about everything? Sed haec vetera; illud vērō recēns, C. Ph., II. 11, 25. Aliquamdiū certātum, S. Iug., 74, 3. Cūr hostis Spartacus, sī tū cīvis? C. Parad., 4, 30.
So also esse, with participles and the like:
Caesar statuit exspectandam clāssem, Caes., B.G., III. 14, 1; Caesar resolved that the fleet must be waited for.
NOTES.—1. The omission of esse is not common with the Nom. and Infinitive.
2. Popular speech omits freely; so, mīrum nī, mīrum quīn, factum, in Latin comedy; likewise potis and pote for forms of posse. To a like origin are due mīrum quantum, nimium quantum, etc., found in all periods.
3. The ellipsis of other forms of the copula is unusual. Thus Cicero occasionally omits sit in the Indirect Question, and Tacitus other forms of the Subjv. besides. Fuisse is omitted by Livy, and not infrequently by Tacitus.
4. The Ellipsis of esse was sometimes due to the desire of avoiding the heaping up of Infinitives. Thus sentences like nōn dubitō tē esse sapientem dīcere (to declare you to be wise) were regularly cut down to nōn dubitō tē sapientem dīcere (to declare you wise).
5. The ellipsis of other verbs, such as facere, īre, venīre, dīcere, etc., is characteristic of popular speech; it is therefore not uncommon in Cicero's letters (ad Att.), in Pliny's letters, and in works involving dialogue, such as Cicero's philosophical writings. The historians avoid it, and it never occurs in Caesar and Velleius.
Allen and Greenough, New Latin grammar is, as often, less exhaustive in its treatment than Gildersleeve and Lodge. The index entry for 'Verbs, Syntax' includes an 'omitted' subentry that refers to section 319.
319. The verb is sometimes omitted:—
a. Dīcō, faciō, agō, and other common verbs are often omitted in familiar phrases:—
quōrsum haec [spectant], what does this aim at?
ex ungue leōnem [cōgnōscēs], you will know a lion by its claw.
quid multa, what need of many words? (why should I say much?)
quid? quod, what of this, that...? (what shall I say of this, that...?)
Aeolus haec contrā (Aen. i. 76), Æolus thus [spoke] in reply.
tum Cotta [inquit], then Cotta said.
dī meliōra [duint]! (Cat. M. 47), Heaven forfend (may the gods grant better things)!
unde [venis] et quō [tendis]? (Hor. S. ii. 4. 1), where from and whither bound? [Cf. id. i. 9. 62 for the full form.]
b. The copula sum is very commonly omitted in the present indicative and present infinitive, rarely (except by late authors) in the subjunctive:—
tū coniūnx (Aen. iv. 113), you [are] his wife.
quid ergo? audācissimus ego ex omnibus (Rosc. Am. 2), what then? am I the boldest of all?
omnia praeclāea rāra (Lael. 79), all the best things are rare.
potest incidere saepe contentiō et comparātiō de duōbus honestīs utrum honestius (Off. i. 152), there may often occur a comparison of two honorable actions, as to which is the more honorable. [Here, if any copulawere expressed, it would be sit, but the direct question would be complete without any.]
accipe quae peragenda prius (Aen. vi. 136), hear what is first to be accomplished. [Direct: quae peragenda prius?]