Zagreus

Zagreus was the first incarnation of Dionysos, in Orphic theology.
Zeus in the form of a snake impregnated Persephone, who gave birth to this "hunter". The Titans used toys to lure the baby Zagreus, then attacked him, tore him apart, boiled and roasted and ate him. They left his heart, though, which was given to Zeus' lover Semele, thereby impregnating her with Dionysos.

Fufluns

Fufluns is an Etruscan god closely related to Bacchus and Dionysos.
He may have originally been a vegetation god later associated with Dionysos. His name appears to have come from the word for "bud" or "sprout", and the Etruscan city Populonia was named for him.
There are numerous Etruscan artistic representations of Fufluns, mostly based on the myths of Dionysos that were brought to Etruria.
There is evidence that Fufluns was also considered a god of the dead.

Bacchus

Bacchus is basically the Roman Dionysos.
There are some differences in character and representation - Bacchus is usually portrayed as young and beardless, and his rites were more simply joyful, drunken affairs - but they are essentially the same god.  
The Roman celebrations of Bacchus were called Bacchanalia, a term that has come to be used more recently to describe any kind of orgy or wild party.
The cult of Bacchus was outlawed by the Roman Senate in 186 BCE.

Sabazius

Sabazius is the Phrygian/Thracian wine god, usually connected to Dionysos. Phrygia was in Asia Minor, where the goddess Kybele originated, and his rites may have been similar to hers. I have not found much information on him, other than one ritual called "god through the lap" where a metal snake was passed under the robes of the initiate. This may be connected to the version of Dionysos' birth where Zeus mated with Persephone in the form of a snake. Periodic festivals called Sabazia were celebrated in his honor. He is also connected with Mithras (another bull-related god). In Thrace, he was considered a solar god, married to Bendis, a moon goddess. Some images of Sabazius show horns on his head.

Yarilo

Yarilo is the Slavic god of sexuality and vegetation, and has some very close correspondences to Dionysos. His name may derive from the root "yary" which means passionate, virile and uncontrolled. He is usually said to be blonde, dressed in white, and barefoot, wearing a crown of flowers and riding a white horse. In one hand he holds a bunch of wheat, and in the other a skull. Wherever he treads, flowers and wheat grow in his wake. As a popular song says: "Where he sets his foot, the corn grows in mountains, where he doth glance the grain rejoices." He is also associated with the god of summer, Kupalo, and with the sun. He had a festival day on June 4, and his death and burial was celebrated sometime during the harvest, possibly at the end of June. A priapic doll was placed in a coffin and carried through the town by an old man after sunset, to the cries and laments of women. He was buried in an open field, after which games and dances began.

St. Dionysius

There are a few Greek Orthodox saints that can be linked to Dionysos, at least etymologically.
St. Dionysius of Zakynthos - feast day: December 17
St. Dionysius the Areopagite - feast day: October 3
St. Denis - The name Denis is linguistically derived from Dionysos.