One of the interesting aspects of the Maori language, as I understand it, is that it includes a class of sentences which not only have no verb, it is positively wrong to form them with a verb.
Does standard English include any non-trivial sentences which have no verb, and are not simply ellipses of sentences which do include a verb?
African-American Vernacular English includes sentences like, "Where you at?", that have no verb. The corresponding sentence, "Where are you at?", doesn't sound like African American Vernacular English. Adding the verb "are" seems to transform it into White American English.
Phrases like, "Hey!" are interjections, and don't meet my threshold of being non-trivial. Answers like "Tomorrow." to "When will you file your story?" seem to be ellipses; in this case, of the verb-laden "I will file my story tomorrow."
I found a related question here in in EL&U, Is a sentence always grammatically incorrect if it has no verb?. The title notwithstanding, the question actually seemed to be asking for an explanation why a certain phrase was in fact not grammatical.
I realise that "standard English" is a bit of a contradiction. Sorry. I refer to any of the mainstream English language dialects, steering clear of pidgins and creoles, where no doubt lurk all manner of interesting grammatical structures.