• Casa d'Ambra on Ischia, one of the best wineries in the region
• Feudi di San Gregorio in Irpina, about an hour east of Naples in the Taurasi region
• Cantina del Mare in Bacoli (near Monte di Procida), where Pasquale Massa makes some fantastic Falanghina (review in Italian).
• Stappo wine bar in Monte di Procida, Via Panoramica 74, 40 47'29"N - 14 03'24"E.
• Cantina Solopaca - Via Bebiana 38, near Benevento, 082-497-7921, Open 8-1 every day, plus 3-8 M-Sat, info@cantinasolopaca.it, they also have "vino sfuso" which you can fill up water bottles or other containers by the liter!

Elsewhere in Italy

Among the most famous wines of Italy are Brunello (from Montalcino, Tuscany) and Barolo (from Cuneo, Piedmont).  For more information about Brunello and Rosso di Montalcino, take a look at the Montalcino travel section.  Other well-known varieties are Chianti (from a large area of Tuscany), Sagratino (Umbria's answer to Brunello), and Vino Nobile di Montepulciano (from the eponomous town in Tuscany).  Also recommended: Amarone della Valpolicella (from Vernona), a robust, full-bodied red and Nero d'Avola (from Sicily), a dark, robust wine from Sicily.  Moio del Massico - another recommended southern Italian wine.

Appellations

Wines in Italy can have VDT, IGT, DOC, and DOCG "appellations"; see the Wikipedia Italian wine page for a good explanation.