Are there any women who were a force of great influence in the Roman Empire?
The most notable would be the Byzantine Emperess Theodora.
Agrippina the Younger, Drusilla and Julia Livilla, appeared on Roman Currency when Caligula was alive.
Agrippina was Nero’s mother (and Caligula’s sister) and helped him become emperor.
Not a Roman, but Cleopatra was certainly a force of great influence in the Empire.
How about Messalina?
Heh, I came in to say these, as I am currently working my way through I*, Claudius*.
Don’t forget Zenobia, the warrior queen of Palmyra, who fancied herself Cleopatra’s descendant (and may really have been).
And what about Augustus’s wife Livia? If you believe Robert Graves, she poisoned 98.7% of the Imperial family.
How about Salome? (Indirectly, of course.)
Does Hypatia count as “Roman”?
Depends what you mean by influence. No women held official positions, but there are tons of women involved in intrigues, accused of having too much power in the imperial house (many of these have already been named, Livia/Augusta is a good example). If you want more examples of that, let me know.
Some people have mentioned foreign queens like Zenobia and Cleopatra - Boudicca, Queen of the Iceni, is a good name to add to that list.
Particular priestesses of the various cults and oracles?
The Chief Vestal may have been influential from time to time.