Festival of Santa Lucia
The festival is held each year in December on the Saint's name day, the 13th. It honors the city's patron saint, who is reputed to have been blind and then have had her sight restored by God's blessing. The festival consists of a procession through the city of a statue of the saint constructed of solid silver. The procession begins at the Duomo and ends at the Basilica del Sepolcro. The statue is so heavy that it takes sixty people to carry it.
Greek Theater Festival
This festival is held every summer from May through July. It has been put on by the Italian National Institute for Ancient Drama since 1913. Performances take place in the Ancient Greek theater in the Parco Archaeologico, and includes classical Greek plays by the likes of Euripides, Aeschylus and Sophocles. What better place to see these plays than in the amphitheatre in which they were originally performed? Tickets are priced according to seating, and range from 30 to 50 euros.
Ortigia Festival
This July festival is a smattering of cultural events that includes plays, ballets, concerts, readings and more. Check out
this site for a schedule of performances (site is in Italian).