Of course everyone in town has their own favorite grocery ... but if you're new to town, or looking for some recommendations... here are my favorite places to shop for particular foods.
Fruits and Vegetables - Without a doubt, North Shore Farms is the place for this. Their produce is fresh and plentiful, and they have pretty much anything you might be looking for from kumquats to tomatillos. They also have pre-made foods -- which my friends rave about, but I haven't really tried. Plus they carry groceries, so if you need cat food or toilet paper, you can get them (just be prepared to pay a little extra for the convenience). Fruit and vegetable prices are very good.
Meat - Uncle Giuseppe's is where I turn to for meat. Their butchers are friendly and helpful, and their meat is fresh. You can see that they take a lot of pride in their meat section, and I never question the quality.
Groceries - Of the two large supermarkets in town, I greatly prefer King Kullen, which is slightly smaller but better laid out. I can get in and out of KK much faster than Stop & Shop, and the cashiers are faster and friendlier as well.
Natural ("healthy") and Gluten Free products - King Kullen has an excellent section of "natural" foods including organic produce, frozen goods, and canned products. You can also find unusual products there -- such as the Juniper Berries that I needed for a certain recipe. In addition, they've expanded their gluten-free offerings as well. Uncle Giuseppe's also has devoted an area to gluten-free foods. And of course, Whole Foods (on Northern and Port Washington Blvds) is an option (although a crowded and very expensive one, so I generally avoid it).