A good question, and I'll break it down into chunks
Roman Kingdom: This is difficult, largely because it's a very murky (not to mention highly mythologised, as shown by the suspiciously long reigns of the monarchs) affair, and its likely that most of the characters that come into play here, like Romulus, Numa Pompilius and Servius Tullius, are highly fictionalised.
Roman Republic: Didn't really have rulers (the Consuls couldn't hold office for very long and powerful figures usually had rivals to deal with), and, really and truly, only 3 men ever managed to 'dominate' the Republic for any length of time; Sulla, Caesar and Octavian (later known as Augustus).
Roman Empire: Augustus, the first and longest reigning Emperor, is certainly up there as a powerful and important ruler. Other early Emperors who should be taken note of as particularly powerful are Tiberius, Vespasian, Trajan, Hadrian, Antoninus Pius, Marcus Aurelius and Septimius Severus. Diocletian is also up there, in fact, he probably ranks second to Augustus in terms of importance, due to the dramatic restructuring of the Empire that occurred during his reign. Also undeniably important and powerful were Constantine and Theodosius (the last men to rule of a united Empire) and possibly Valentinian I.
Eastern Empire: Anastasius, Justin and Justinian were all highly important (although, perhaps, not as powerful as traditionally made out to be). Heraclius is another important Emperor (for his military skills and phasing out of Latin as the language of governance), and both Basil's also count as powerful certainly. Alexius I and Manuel I of the House of Comnenus were also rather important for the role they played in stemming the Byzantine decline (or pushing it back, if one were to be ungenerous).
This is a rather rough answer, I may give more detailed ones though
