Volpetti, Via Marmorata, 47 in Testacchio and Via della Scrofa, 31 (in historic center).
Deli and food shop with lots of cheese, olives, wine, olive oil, bread, etc. Also a Tavola Calda (prepared hot foods that you can take home). You can order a complete meal to take home. The one in Testaccio is the main shop and the largest. The Via Scrofa one is smaller, but still very good.
Gelateria della Palma, Via della maddalena 20-23, two blocks from the Pantheon.
I don’t like the gelato here, but they have the best candy store! Take a bag from the stack and fill it with candies that they weigh for you (I don’t think you can mix the types of candies). My favorites were by Feletti (Bon Bon Pera Ricoperto di Cioccolato – hard candies that are a chewy chocolate around a fruit center) and the chocolate covered Rum truffle type thing.
Confetteria Moriondo & Gariglio, Via del Pie di Marmo, 21-22, tel:06-6990-856
Supposed to be an excellent chocolate store. I hope to report more later.
Biofood, Via di S. Francesco a Ripa. Good selection of grains, food products, produce.