Poetry is such a unique form of literature, and I'm not trying to belittle it, but sometimes it seems as though in modern times the only ones who appreciate it are fellow poets.
You're going to very quickly run into the problem of genre. If you look back far enough, it can become difficult to neatly separate poetry from song from verse drama.
In the western canon, you can trace it all the way back to Homer (c. 850 BCE) and Sappho (c. 630 BCE). In East Asia, there are verses about as old if not older. In South Asia, the Vedas from c. 1500 BCE are in verse.
As for mass appeal, I'll hit on a couple of famous periods in drama. Greek drama was very much a civic matter with broad popular support among the citizen class, and was written in a spoken/chanted/sung verse.
In Shakespeare's time, the drama was a very popular art form and was usually written in iambic pentameter or another verse form (for a long time it was the 12-syllable line favored by Corneille and Racine in France).
In both cases, we can see a popular drama that was constructed in a poetic fashion. It may not resemble contemporary poetry in some important ways, but they would have absolutely fit into the ideas of poetry at the time of writing.