As a general rule sentences without a verb are incomplete sentences (sentence fragments). But the exclamatory sentence form is considered a grammatical sentence even though there is no verb. For example 'How sweet!' 'What a mess!'

A sentence in English must have a verb to function - it is impossible to make sense without one. The only time it's acceptable is in what is known as fragmentation in literature; "He stood still. Silence." ; in which "silence" is shortened from 'there was silence' or 'it was silent' for dramatic effect.

I agree with both comments above. I guess you've found only short sentences - interjections - which imply a verb instead of stating it. For 99.99% of the time, you need a verb.