Like the Egyptians, the West Asians, the Carthaginians, the Greeks and the Etruscans before them, the Romans built many temples for their gods. One of the first buildings we know of in Rome is the Capitoline Temple, which was built on top of the Capitoline Hill under the kings of Rome. It was a temple for three gods, Jupiter, Juno and Minerva. But that temple has been completely destroyed, and only little bits of the foundations are left today.
During the Republican period (500-1 BC), Roman generals built hundreds of temples all over downtown Rome. These temples were mainly built to thank the gods for the generals' victories in war. They were built all along the sides of the Via Sacra (the Sacred Way) that the generals marched along when they came back to Rome to celebrate their victories. Again, most of these temples have been destroyed, but there are still a few of them around.
(Thanks to Lynn Lichtenbaum for this picture)
These two pictures are of the same Republican period victory temple in Rome.
It is built in the Ionic style, but like Etruscan temples it stands on a high base, with a lot of steps in front leading up to the temple. Also, notice that the columns are stuck to the wall in the back, instead of being free-standing all the way around as they are in Greek temples.
Learn by doing: build a Roman temple out of Lego
Roman Republican Temples
City : A Story of Roman Planning and Construction, by David Macaulay (1983). For kids - brilliant!
Roman Architecture, by Frank Sear (1983). The standard college textbook.
Roman Imperial Architecture, by J. B. Ward-Perkins (1992). A more detailed textbook, and harder going.
The Architecture of Roman Temples : The Republic to the Middle Empire, by John Stamper (2004). 052181068X