As a herm, where you only see the head and an erected penis (herms are quite common; Hercules herm, a headless herm and a herm from the Athenian Agora.
As an old, manly god, resembling an eastern ruler with long curly hair, a beard and sometimes a diadem. Notice the wines in his hair.
This piece is from the 2nd century AD, Rome.
The infant Dionysos, such as seen in the very famous group Hermes and the Dionysos Child by Praxiteles. More information on this piece can be found here.
As a young god, with slightly female forms. From the 2nd century AD, Rome.
He can also be found with rams or bulls horns on coins.