How have Roman culture influenced later cultures?

Roman culture was greatly influenced by both the Etruscan and Greek cultures.

Etruria and Greece. The Roman culture originally came from the Eurtruscans and was later influenced by the Greeks when the Romans conquered them.

Greece

The Roman gods were inspired by the Greek gods (eg. Zeus became Jupiter). They were the same gods with different names.

Religion, Armor, Weapons and Theater. Among many other things.