USS Einstein wrote:
The Romulans were influenced by Rome, but also by other cultures, perhaps including Imperial Japan.
But what is most important in making a species believable, is making their culture rational and pragmatic. So, the Romulans are not a like-for-like model of the Roman Empire in space. Rather, we can perhaps infer, they have arrived at a similar culture through practical necessity.
Rome's system arose because it's rulers desired conquest, but had no justification for calling Egypt or Greece a part of Rome - they were foreign lands, and everybody knew it - and there was no Eastern concept of 'universal empire' in which nations became irrelevent, because Rome was rational and not given to idealistic flights, so instead the new territories became provinces, overseen by the senate, with regions governed by Proconsuls, etc. Wars were justified in terms of defence, often, as is necessary in an imperial democracy. We can perhaps infer that when the early Romulans entered space, starting as little more than thugs, they needed an imperial system by which a senate that only governed Romulus could govern other species - so their system of an imperial military, and proconsuls, etc, arose.
The 'Space Romans' analogy worked better in TOS than in TNG and later. And, it only works if you think of Rome as first century Rome.
In TNG/DS9 I think they were meant more to be the USSR. A secretive, closed off, militaristic society with secret police who disappear people. In a cold war with the Federation, playing spy games with the Federation and Klingons, portrayed as wanting a war but not wanting to be viewed as the instigators.
There are some very visual and some superficial connections to Rome and Romulans, but we must remember that Romulus and Remus are the Earth names for Romulans\Remans. Romulans and Remans, don't call themselves that in their own language. I also always thought that the 23rd century Romulans were more like the honorable adversary, rather than the enemy, and are almost sympathetic (like in Balance of terror). The 24th century Romulans are less sympathetic, less honorable, and less Vulcan-esk, too
Also, I had always felt that during TOS, the Romulans were the cold war analogy to the Communist Chinese, and the Klingons were analogous to the USSR, too.
During TNG yes they became more of a stereotypical villain. During first run, it was hard to compare the Romulans to any power in the post-Cold War era of the late 1980s and 1990s, but in retrospect, I think they can almost be compared to North Korea, if North Korea was an actual empire.