Rome absolutely did borrow things other than styles of clothing from other cultures. Most notably, Rome borrowed many things from the Greeks. They also borrowed some aspects of other cultures.
Perhaps the most famous way in which the Romans borrowed from others was in religion. Roman religion was heavily influenced by Greek religion. This influence came to them through the Etruscans. The Etruscans adopted the Greek gods and those gods were then adopted by the Romans. The Romans came to have equivalents to all the major Greek gods (Jupiter for Zeus, Mercury for Hermes, etc.). Later on, the Romans also came to borrow religions from other cultures. Romans came to adopt religions from such places as Egypt and Persia. In these ways, they were borrowing from others.
Rome also borrowed heavily from the Greeks in terms of education. Roman children (of the elite classes) were often taught by Greek slaves. The things that they learned were patterned after what the Greeks thought important in education.
The Romans also borrowed from the Greeks in the arts. They translated Greek plays into Latin. When they wrote in Latin, they often followed Greek traditions and plots. They also adopted Greek styles in things like painting and sculpture.
In short, the Romans borrowed liberally from other cultures, particularly the Greeks.