Tiber Island/Isola Tiburina: You can explore Rome's Tiber Island in a few hours, and, since it is the only island that lies within Rome's boundaries, you can then say that you have done all the islands in Rome. There were once other islands in the swampy area of the Campus Martius, but already in ancient Roman times the swamp was mostly drained and leveled. Later flood control measures and raising of the ground level have dried the Campus Martius.
You can reach the Tiber Island from either side of the river. It's possible to drive over from the Trastevere side on the Ponte Cestio road bridge, a rebuilt version of the 46 BC bridge built by Lucius Cestius, but it's doubtful you would find a space among the thirty or so parking positions on the island. Much more pleasant is the walk across from the Piazza Monte Savello, near the Ghetto and the Theater of Marcellus, via the pedestrians-only Ponte Fabricio, the oldest Roman bridge that survives in the city. It was built for Lucius Fabricius in 62 BC and is still pretty much the way he built it. This bridge has long also been called the Ponte dei Quattro Capi by locals because of the two four-faced Janus herms that are mounted on the parapet of the bridge. (Janus is usually two-faced and looks up and down the road. Four-faced Janus images guarded only the most important intersections -- in this case of the River and the strategic road over the bridge.) If you walk to the island across Ponte Fabricio you will see on your right the 17th century rebuilding of the church of San Giovani Calibata and on your left the still impressive 11th century Pierleoni (later Caetani) tower and the fortress. The Pierleoni, a converted Jewish family, eventually produced Pietro Pierleoni who was elected Pope Anacletus II in 1130. Mostly because of his Jewish heritage, France and Germany rejected Anacletus and supported the Papal claim of Innocent II. Anacletus and Innocent eventually died and the papacy was reunified by a new election in 1138. Anacletus is counted as an "anti-pope" although the church now records the fact that he was elected by the majority of the Cardinals.
The island is really quite small, about 67 meters wide at its widest point and 269 meters in length, but it has a very long history. According to an ancient Roman legend, the island formed over the wreck of a ship that sunk before the founding of the Roman republic in the 8th century BC. Although actual evidence is lacking, it's possible that the legend is true, since the island really is a silt bank that formed in the bend of the river, just as one would form downstream of an obstacle. Even today, when the river rises Tiber Island accumulates a burden of flotsam (natural stuff that floats into the stream) and jetsam (manmade stuff that gets thrown into the stream). All of it is removed annually to avoid periodic disastrous blockages of the River. How disastrous it might be is demonstrated by what happened after Nero's "cleanup" of Rome after the fire -- he dumped the debris into the river above Tiber Island. That caused a serious flood of the Campus Martius and, when the debris finally broke loose, the surge caused a very expensive change in the river's course down at Ostia. Presumably flood-control measures taken since Nero's time and especially in the last hundred or so years could lessen the impact, but why take chances.
Archeologists say that the oldest human settlement in the Rome area was on the island -- it originally was the safest spot around. Eventually, as weapons' throw-weight and range improved, it became necessary to control the overbearing Capitoline Hill, and, if you were going to do that, you might as well move up there and fortify your positions in earnest. That happened in the 9th-8th centuries BC by latest estimates. The island retained strategic and commercial value, however, and was always used for something. Early on, Romans determined empirically that isolation of diseased persons limited contagion, and the island became, first, a place to abandon the sick and, eventually a place to treat them.
The Aesculepius legend later associated with the island is the way Romans explained the quarantine function. The story goes that a plague was raging through Rome in the middle 290's BC, and, after consulting the Sibylline oracular books, the Republican government sent a delegation to the Aesculepion in Epidaurus, Greece, to retrieve an image of the healing god. The ship returned to Rome in 291 not only with the desired image but also with a huge snake (a major symbol of Aesculepius) that had come aboard and nestled in the cabin of the head of the delegation. The question of where to house the newly arrived idol, which had been avidly discussed both on board and ashore, was peremptorily decided by the serpent, which slipped over the side and swam to the island. A new temple to Aesculepius was built on the spot where the snake made its new abode next to a spring, and the spring, being thus sanctified by Aesculepius, was said to have healing powers.
The remains of that Tiber Island Aesculepion are thought to be under the church on the downstream end of the Island. The Holy Roman Emperor Otto III dedicated the first church on the site to St. Adalbert at the end of the tenth century, but Otto is also said to have enshrined the relics of St. Bartholomew the Apostle in the church. Adalbert was soon forgotten and the church acquired the name of St. Bartholomew, perhaps because Bartholomew, according to popular mythology, had been skinned alive: his resulting supposed protection of people with skin diseases tied in neatly with the island's medical tradition. Inside the church is a carved wellhead, which, some say, marks the spot of the spring of Aesculepius and the snake. Nineteenth century excavations under the church, in the course of one of its many rebuildings, found many artifacts associated with the cult of Aesculepius.
Once the church complex took over the cult site, a new medical center was needed, and it gradually grew until now the entire upstream end of the island is covered by the modern hospital. It was in an earlier version of this hospital that, according to legend, Rahere, a roisterous member of the court of King Henry II of England, recovered from malaria and had his vision of St. Bartholomew. That reformed him, made him a monk, and caused him to found the great hospital of Saint Bartholomew in London in 1123. Since 1548, St. Bartholomew's hospital on Tiber Island has been administered by the Fatebenefrateli religious order of monks -- their name means "do-good Brothers".
The Tiber Island is now completely surrounded by a modern stone-over-concrete platform, which you reach by a stairway on the Trastevere side of the island, near the hospital entrance -- it's across the piazza from the church of St. Bartholomew. The platform, especially on the Trastevere side of the Island, accumulates a lot of debris between annual pre-winter cleanups, but it is usually cleared by the end of November.
A walk around the island on the platform is quite pleasant. A slow circumambulation takes less than three-quarters of an hour, unless you dawdle, as we did, at the small dams to hear the rushing water and to see the impressive undertow. (Under no circumstances should you enter the water anywhere near those dams when the water is running high. We watched as the undertow repeatedly pounded a telephone-pole-size log down to the bottom -- we could hear it strike and feel the ground shake. The police station on the island maintains small rescue boats, but, because of the undertow, they are more likely to recover remains than effect a rescue.)
There are two other things to see while walking around the platform.
Under a stairway leading up to the police station on the island's downstream end is the remnant of the ancient Roman travertine decoration of the Island as a warship. You can see the ship's prow with its protruding ram (rostrum) and Aesculepius' snake climbing aboard. From the same end of the Island you can also get the best available view of the Ponte Roto (Rotten Bridge), which is the only remaining arch of the ancient Ponte Aemilius build in 179 BC by Marcus Aemilius Lepidus, who also built the Basilica Aemilia in the forum.
Pictures of the Island, its bridges and other Tiber River features: http://catholic-resources.org/AncientRome/index.html
The "unofficial" Tiber Island Internet site: http://www.isolatiberina.it/
Old prints and new pix of the Island -- the oldest of which (1491) clearly shows the flour mills that once took advantage of the fast current around the island: http://www.isolatiberina.it/B_IsolaT01_e.html, and http://www2.siba.fi/~kkoskim/rooma/pages/TISOLATI.HTM
Tiber Island Maps, old (1551) to recent (1993): http://www.isolatiberina.it/Mappe_e.html