The Esquiline was the largest of the 7 hills of Rome. Its claim to fame comes from the Roman emperor Nero who built his domus aurea 'golden house' upon it. Before the Empire, the eastern end of the Esquiline was used for dumping refuse and the puticuli (burial pits) of the poor. Carcasses of criminals executed by the Esquiline gate were left to the birds. Burial was forbidden within the city proper, but the burial area of the Esquiline was outside the city walls. For health reasons, Augustus, the first Roman emperor, had the burial pits covered over with soil to create a park called the Horti Maecenatis 'Gardens of Maecenas'.
The Colossus, Temple of Claudius, and Baths of Trajan were all located on the Esquiline.
Mary Beard, classicist and columnist for the UK Times, lists the following 10 hills of Rome: the Palatine, Aventine, Capitoline, Janiculan, Quirinal, Viminal, Esquiline, Caelian, Pincian, and Vatican. She says it is not obvious which should be counted as the 7 hills of Rome. My list is a standard one, but she does, or course, have a point.
The area of the Palatine is about 25 acres. It is the central hill of the seven hills of Rome. It was the first hill area to become a settlement. Much of the Palatine has not been excavated, except for the area nearest the Tiber. The residence of Augustus (and Tiberius, and Domitian), the Temple of Apollo and temples of Victory and the Great Mother are there. The exact location on the Palatine of Romulus' home and the Lupercal cave are unknown.
Update: BBC News' 'Mythical Roman cave' unearthed reported, on November 20, 2007, that Italian archaeologists think they've found the Lupercal cave, near the palace of Augustus, 16m (52ft) underground. The dimensions of the circular structure are: 8m (26ft) high and 7.5m (24ft) in diameter.
The Aventine Hill became the home of the plebeians. It was separated from the Palatine by the Circus Maximus. On the Aventine were temples to Diana, Ceres, and Libera. The Armilustrium was there, too. It was used to purify arms used in battle at the end of the military season [Mommsen]. Another significant place on the Aventine was Asinius Pollio's library.
The Capitoline is the smallest in area, 460 meters long and 180 meters wide, situated between the forum and the Campus Martius. Its name comes from the legendary human skull (caput) found buried in it (Livy I.55). It was the home to the temple of Iovis Optimi Maximi (Jupiter best and greatest), built by the Tarquin kings of Rome.
The Quirinal is the most northerly of the seven hills of Rome. The Viminal, Esquiline, and Quirinal are referred to as colles, more diminutive than montes, the term for the other hills. In early days, the Quirinal belonged to the Sabines. The second king of Rome, Numa, lived upon it. Cicero's friend Atticus also lived there.
When the Gauls attacked Rome, the Capitoline did not fall because of the geese who gave warning. The temple of Juno Moneta, possibly named moneta for the warning of the geese, is also on the Capitoline. This is where coins were minted, providing the etymology for the word “money”.
The assassins of Caesar locked themselves in the Temple of Capitoline Jupiter after the murder.
Criminals were dropped from the hill onto the Tarpeian crags below.
A small, unimportant hill, with few monuments. Caracalla's temple of Serapis was on it. To the northeast of the Viminal were the thermae Diocletiani, Baths of Diocletian, whose ruins were re-used by churches (now the Basilica of Santa Maria degli Angeli and the Museo Nazionale Romano) after the baths became unusable when the Goths cut the aqueducts in A.D. 537.
The Baths of Caracalla (Thermae Antoniniani) were built south of the Caelian Hill, which was the most south-easterly of the seven hills of Rome. The Caelian is described as a tongue “2 kilometres long and 400 to 500 metres wide” in A Topographical Dictionary of Ancient Rome. The Servian Wall included the western half of the Caelian in the city of Rome. During the Republic, the Caelian was densely populated. After a fire in A.D. 27, the Caelian became home to Rome's wealthy.