"Slow Food" is a term meant to contrast with "fast food." These are the merchants I frequent for food.  Some of these producers also sell on-line.  If you trust me, you can trust these producers.  My interest in all this was piqued by lecture I attended by Nina Planck and her book Real Food.  If your interest is similarly piqued, I recommend Slow Food USA as a resource for those dwelling in the United States.

• Anson Mills - my primary supplier of whole grains. They are in South Carolina, I only shop mail-order.
• Astor Wines - my most-favored wine store for bargains.
• Catskill-Merino Sheep Farm - I can personally attest that Eugene Wyatt is the kind of guy you want raising your lamb, plus they hand-die yarn.  Also at Union Square Greenmarket.  His sausage-maker is a true artisan.
• Crush Wines - my most-favored wine store of quirky and small producers
• Flying Pigs Farm - raises heritage breeds on a clean, humane, sustainable pig farm.  This pork tastes so much better.
• Grazin Angus Acres - Grass-Fed and Finished Black Angus raised on a sustainable farm.  Unfortunately for those distant from the NYC area, to avoid excessive and unecessary consumption of fossil fuels, Grazin Acres won't ship their product long distances.  Try to find such a producer in your local area. Look for pasture-grazed cattle, not finished on corn (unfortunately, "organic" means nothing in this regard).  This is the best beef I have had in the United States (second only to Tuscany in the world in my experience).  At Union Square Greenmarket.
• Murray's Cheese - I didn't know cheese before I met Murray's.
• NYC Greenmarkets - If you live in New York City, you are as lucky as I.  You can buy your food from the people who grow it.  I shop weekly at the Union Square Greenmarket.  
• Ronnybrook Farm Diary - Diary farming, hopelessly out of date, and proud of it.  At Union Square Greenmarket, among other places.
• Zabar's - A foodie deli, always reliable.