Roman architects didnt really have a style of their own. They stole ideas and concepts from the places they conquered. After "borrowing" these ideas, the manipulated them to suit their own purpose. They were able to add some positive elements such as concrete and the aqueduct. The aqueducts are basically all thats left of the ancient architecture of the Romans. They are unique because this was the first time arches were used extensively in a project. The Greeks never fully realized the potential of the arch, but the Romans succeeded, and used it extensively.
The most important building in a Roman city was probably the forum. The meeting place for business people, and a place to shop, it was the center of town. Civic buildings, such as a basilica, lined the sides. Near the end of the forum, a temple usually stood. The early temples were top heavy with wide eaves and bulky decorations. The later temples used the Greek proportions. They were lighter and more graceful. Corinthian columns were the most popular type of column for the Roman temples. Sometimes theaters lined the sides also, but unlike Greek theatres, they had supports for the seats. Amphitheatres such as the Colosseum were elliptical in shape, and recessed. Public baths were near the center of a city, and represented an important part of Roman life. They were huge symmetrical buildings with sunken in pools and high vaulted ceilings.
Roman homes were extremely varied. Generally, the rich Romans had nice houses, and the poorer ones had smaller, simpler houses. A simple Roman house was several stores high, but very skinny. Larger, more elaborate houses sometimes had gardens in a small courtyard in the house that was open to the sky. In extremely rich peoples houses, the indoor courtyard was an atrium, that sometimes connected to a lake and garden outside. If you want to go out and rent a movie set in this era, "A Funny Thing Happened on the Way to the Forum", is a pretty good film with some very well done Roman houses in it.