Some of them are spurious. In the Roman Forum a short distance from the Mamertine there is a building labeled a "supposed Carcer". The signage basically admits that this was simply a misidentification of the site of the Mamertine. If I read it properly there seems to have been suspicion that it was actually a brothel.
On a somewhat more uplifting note, there are numerous sites that relate to the known imprisonments of Saints Peter and Paul.
Although it is seldom open and in a very seedy neighborhood, a quick stop in to visit the Basilica of Saint Peter in Chains would be in order. It has a set of ancient chains said to be from Peter's captivity in Jerusalem. Yes, the very ones that miraculously fell away when an Angel of the Lord told him to stand up and walk away from his imprisonment. There is also a rather nice statue of Moses by Michelangelo.
Since "house arrest" was actually more common in the Imperial era it is not surprising that several sites claim to be the location where Peter, Paul or both were held while awaiting trial. Any such private dwelling would of course become an early place of pilgrimage and worship. The Church of Santa Maria in Via Lata makes a plausible claim but without solid documentary or archaeological evidence.
For a site that is a lot more fun, and which has tons of history piled up in layers, I highly recommend San Nicola in Carcere, literally, Saint Nicholas in Prison.
It is a fabulous example of continuity and recycling. Here is a photo showing the church literally built into the ruins of several Republican era temples.
San Nicola is actually built of, into and over the ruins of no fewer than three Republican era temples, specifically those of Janus Bifrons (260 BC), Juno Sospita (circa 195 BC) and Spes (date uncertain but restored in 213 BC). Spes is one of my favorite pagan deities. The name means "Hope" and her depiction on coins is generally a winsome lass in a long skirt....which she is slightly but intentionally lifting!
San Nicola is a quiet little place, it took me a while to find someone who would let me into the crypt area beneath the church. There was a small fee and you got a brief guide pamphlet to help you out. OK, lets get down and Roman!
The crypt entrance is suitably creepy. And down below I was able to wander about as I pleased.
Unlike most such sites in Rome there is no prohibition on photography. And having the place to myself I got to experiment a bit with flash and non flash options. The flood lights did complicate lighting somewhat, and in one location I actually encountered this:
Standing inside an ancient Temple I am looking out past a Republican era column. Light peeks in from a tiny niche. A hardy weed grows in it and the raucous sounds of Roman traffic faintly intrude on the general silence. I was unable to find this spot on a careful survey of the outside areas.
Now, what would you actually expect to find in a "Carcer", a prison? Something like this perhaps?
Sure, why not. There are in fact piles of human bones laying about. The green color is from algae that always grows in underground places where, as in this case, a flood light has been installed for your viewing convenience.
Alas for dark, Gothic mystique. These are not the bones of prisoners. In Medieval times it was a burying place for monks.
In fact, San Nicola quite likely was never a prison at all. The initial dedication was to St. Nicholas, Bishop of Myra, who as the initial inspiration for Santa Claus is not generally associated with "doing hard time". The addition of "Carcere" came later. There is a single reference in Pliny to there being a prison somewhere in this neighborhood, but it would have been centuries before the first church was established here (felt to be very early, but with an architectural Frankenstein like this, who can say!). As this was a part of the city that was occupied continuously, there is also a notion that during the Gothic Wars it may have been a place where unreliable folks, or those unwilling to contribute money to the defense of the City, may have been held. And finally the series of small rooms you can see above made those with imaginative minds - and a few historical hints to play with - see jail cells when in fact they were most certainly small offices associated with the cult worship.