Language. The language we use today was developed from the Romans. The Romans wrote and spoke in Latin and many of our words are based on Latin.
The Calendar. Started by Julius Caesar it is based on the Eaths movement around the sun. The names of the months where taken from the names of Roman Gods and rulers. July is named after Julius Caesar himself.
The Romans also gave us:
A legal system and laws
Aqueducts (bridges for water).