Many of the earrings found in Ancient Rome are based on Hellenistic styles. The hoop and drop earrings being quite popular in the archeological record. Below are some of the different types. (The abbreviated version)
Oval Hoop Style
This is influenced by the greek Hellenistic style, but simpler.
Gold and Banded Agate Earrings
Crescent Shape Style
Another style influenced by the Greeks.
Gold and Emerald Earrings
Hoop
Simple hoop earrings like this could be permanently closed for those only having on pair.
Gold Hoop Earrings with Rock Crystal
Drop (Dangle-y)
This style of drop pearl has one to two earlier by the second century we see more of the three drop pearls.
Gold Bar with Pearl Drops Earrings
Cluster
Pearl and emerald cluster earrings found in Pompeii, thus they were around in the 1st century if not earlier.
Emerald & Gold Cluster Earring
Other Types
This dangle style earring can be seen in the Hellenistic and Etruscan styles. Many pieces of jewelry are influenced by the hellenistic styles but a simpler interpretation.