From the time of Augustus to the end of the 5th century AD Rome had around 150 emperors. Many are familiar with such figures as Constantine the Great (who by the Edict of Milan recognized Christianity and ended their prosecution), or Nero (who is said to have started the fire that burned down half of Rome, because he needed room for his new palace), or Claudius (who was a bit dim and hence his life was spared, but turned out to be a very good administrator, for a while).
There are however many emperors, such as Postumus, Probus or Gratian, of whom most have never heard of, and of whom only historians or coin collectors of the period will be familiar with. There are also those that are very obscure, such as Silbannacus (c. 248 AD), who are known to have existed from a single unique coin, and of whom absolutely nothing is known.
The portraits of the emperors on their coins can give you a very good idea of how they looked like, especially before the late 3rd century, after which the portraits became more and more stylized, making it harder to distinguish emperors.
Most historians will draw a line during the reign of Anastasius (491-518 AD) as the end of the Roman Empire (more specifically, during the reform of c.496 AD), and the beginning of the Byzantine Empire. These correspond to the Western and Eastern sides of the Roman Empire, which took different paths, with one emperor usually being in charge of each side.
After the death of Constantine the Great, dynastic quarrels greatly contributed to the splitting of the Empire into two pieces. It was Constantine the Great who rebuilt the ancient city of Byzantium, renamed it to Constantinople, and made it the new capital of the Eastern Empire in 330 AD. Also, by making the Empire Christian, he altered forever the content that was put on the coins; over time the pagan gods disappeared, to be replaced by symbols of Christianity.
However, coins retained a highly militaristic element for quite some time. Eventually the Western Empire collapsed, and over the next 1100 years the Byzantine Empire prospered (of which subjects did call
themselves Romans), until the Ottoman Turks put an end to it in 1453 AD. During the inept reign of Honorius Roman power greatly suffered due to constant attacks of barbarians from the north. The coins after his reign take on a different appearance (with less interesting types), and start to shrink to almost microscopic size. The mint in Rome, which has operated since the beginning of coin making days during the Republic, was finally closed during the reign of Zeno (474-491 AD).
It is however totally hopeless to try to collect a coin of every single one of the Roman emperors that ever lived. There were a handful of emperors that lasted only a few days or weeks, which didn’t give them enough time to strike coins in any substantial quantity, if any. Some are known from unique coins in the British Museum, some from very rare pieces in museums or private collections.
However, these people did not contribute to Roman history – they were declared emperors by their troops on some military expeditions, only to be murdered shortly after by the same troops! It is interesting to note that about a third of the emperors below were murdered, and only about a third died of natural causes like old age, or a plague! Others were killed in battle, or killed themselves, mostly to save someone else the trouble of killing them… Probably during certain times it must have been dangerous to be called an emperor!