The list of essential Klingon episodes made me ask a similar question about Romulan episodes.
A discussion on Quorra yields Balance of Terror, the Defector, In the Pale Moonlight, The Enterprise Incident, Unification, Face of the Enemy, Inter Arma Enim Silent Leges, and The Enemy
I disagree with In The Pale Moonlight, it's not really a "Romulan episode", just an episode that has Romulans in it.
A reddit thread yields:
TOS: Balance of Terror, The Enterprise Incident
TNG: The Defector, Unification
DS9: In The Pale Moonlight, Inter Arma Enim Silent Leges (again, the Romulan culture was completely incidental in these two episodes, DS9 really didn't use the Romulans as anything other than plot devices)
VOY: Message in a Bottle (it could've been any antagonistic TNG race, the Romulans were plot devices again)
As a side not-quite-PNQ: Can you think of another way the Romulans could've been used besides as generic antagonists or "evil Vulcans"?
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