Generally, Roman Criminal law didn't recognize (public) imprisonment as a valid category of punishment. This is true for all times until late antiquity. Public prisons and an associated system of imprisonment as punishment as we know them today are largely a development of the 18th century. In ancient times, corporal or capital punishment dominated, and prisons only served to contain the accused until his sentence or the convicted until the execution of his punishment - the most famous example being of course Sokrates, who appears prominently in his talks with his friends and disciples in prison before his execution.
A prominent use for imprisonment (in Roman legalese this is termed in vincula publica duci, 'to bring into public shackles') was related to coercion. The consuls had the power to throw people in shackles to coerce them to comply with their orders. Cicero (de legibus III, 6) recounts how imprisonment or monetary punishment were possibilities for Roman magistrates to enfore their will, of course limited by the veto of other magistrates of the same or higher rank as well as the possibility of provocatio, that is calling upon the popular assembly to acquit. Acting against these limits, or otherwise illegally imprisoning a Roman citizen at the time of the legal scholar Paulus (Paul., Sent. 5, 26 1f.) would lead to execution for those of lower status and exile for those of higher status. This was no sentence, it was just one of the methods of coercion available to magistrates, which had its limits in the other magistrates and the popular assembly.
One of the main uses for imprisonment was too keep the convicted secured until his execution. Now this is not a prison sentence per se since it only served to ensure the eventual punishment in the form of execution by preventing the convicted from escaping justice. However, in practice, there was no limit on how long someone could be imprisoned awaiting his execution. Thus, in effect, this could see a capital punishment mutated into imprisonment for life de facto if not de jure - in essence, what Caesar proposed for the conspirators of Catilina (by proposing to prohibit anyone from prosecuting their case, thus keeping them in remand indefinitely).
De facto, imprisonment was also the consequence of the second most severe punishment (after capital punishment) the Roman justice system could impose, the damnation to work in the mines (usually for life, though there was the possibility of release after 10 years if the convicted had become 'unsuable' - though without restoration of his civic rights). The convicted did their work in chains and were confined to their barracks, so in essence it was imprisonment with hard work.
The same is true for the milder form of this punishment, to work on public works, such as streets, the cloaca, service in the public baths, bakeries and spinneries (mostly for women), usually for three or ten years only, which again in essence was imprisonment with light (in comparison to the mines) work. These two forms of punishment were de facto equivalent to imprisonment, thus it is not very surprising that Roman Criminal law never developed a system of prison sentences; members of the upper strata could be exiled and thus suffer an equivalent punishment, since often they were under military guard.
In essence, public imprisonment in Ancient Rome was limited to remand and 'death row'. Late antiquity is a bit of a different matter, since it seems that imprisonment became more popular among some governors, and the amount of imprisoned increased. Slaves and debtors were also increasingly held in public prisons (debtors normally were in private debtors prison). But I'm not too qualified to talk about that period - we've got others here who can, though.
One thing one has to keep in mind is that Roman criminal justice was different in many aspects from modern systems. There were no prosecuting attorneys, and it was mainly in the hands of the damaged party to prosecute the perpetrator - which in many cases led to lynching and vigilante justice. Private prisons were a thing (mainly for debtors and for slaves, though these were increasingly regulated and outlawed in the later empire, and probably not as prevalent as was believed for a long time among historians), and until Augustean times the pater familias had a high degree of jurisdiction over his family - up to and including capital punishment. Provincial governors had liberties in which punishments they handed out, but imprisonment as a sentence in itself was probably very rare and is only known from isolated cases (e.g., for forcing others to gamble, for fortune tellers and prophets that incite the population, for the insane).