If you're looking for "foreign" products and spices remember to check out the Hello Market, the Romanian/Moldavian markets as well as the North African and Chinese markets behind via D'Azeglio (oltretorrente).
Also, we've recently learned you can make real Brown Sugar at home - just pick up your molasses at the Ceres Bio Store!
Cheese: Rastelli, via Copelli 2/E and Paradiso del Formaggio, Borgo del Gallo. Good selection of French and Italian cheese, and of course prosciutto di Parma. Cheddar can be found at Casa del Formaggio, strada Nino Bixio 106.Bread: if you're tired of the 'tipo 0' carton-like bread... try the 'pane di semola' made by Panetteria Alinovi, via Carducci 3. You can find tumeric bread now in many bread shops in Via Farini, along with brown breads and cereal breads. Pane pugliese and pane arabo are also acceptable options.
Fresh from the day organic eggs: Motta, via Carlo Goldoni 2NaturaSi Supermarket: For vegetarian products, gluten free products, etc. Via La Spezia, 72/A.
Ceres: Vegetarian and bio products. http://www.bioceres.it/ Borgo delle Colonne, 8.
Natura & Sapori: Organic fruits, vegetables, and other related products. In Via Farini and Strada della Repubblica
Farmers' Markets: fruits, vegetables, fresh produce, in strada Imbriani, Saturday 8:00 am - 12:00 pm.
The Fruit & Vegetable store at the beginning of Via Farini can be expensive but offers great produce and often has such rarities as "Mexican or Israeli Avocados", "Parsnips", "Fresh Dill", "Dried Cranberries" and even real North American "Sweet Potatoes".
La Gourmanderie: strada XXII Luglio, 8. French delicacies, champagne, foie gras, terrines, freshly made macarons...
Pasticceria Al Caruso, via Pertini 12/D, also makes delicious macarons (as well as pastries, chocolate, made to order buffets).
Picard Surgelati, via La Spezia 72/A: originally a French chain of frozen food; the product line is very much "italianized", but they also propose some French specialties (you MUST try the moelleux al cioccolato!) as well as international fair such as "Edamame beans" and "Indian Vegetarian Samosas"Hello Market (Thai, Chinese, English, Indian) food, viale Mentana (check the freshness and expiry date of products!). Curry Paste, Coconut Milk, Heinz ketchup, Heinz Baked Beans, Quakers Oats, Ribena, Condensed milk, Panko et al.
Esselunga supermarket offers online shopping with home delivery. Esselunga carries the largest selection of non-Italian food in Parma (e.g. real Dijon mustard, Lurpak Danish butter crème fraiche, Tabasco sauce, curry powder, coconut milk, sushi, wasabi and ginger for sushi, tahini sauce and dressing, Hellman's real mayonaise, Brown sugar (with molasses), good Oral-B dental floss) those little details that can make your day!), both online and in stores.
Punto Simply, via Verdi, offers some of these products and is more central, and open on Sunday.
Campus Conad - Skippy Peanut Butter
If you are really desperate for foreign products, you can shop at the Superpolo supermarkets in Milan which carry those items - like baking powder, brown sugar, chocolate chips cookies, pumpkin filling, tofu, etc. - which are difficult to come by in Italy. There is also the California Bakery with a real American (expensive!) brunch and bagels.