Asia Supermarket does encompass Asian foods and chinaware.The prices are good, the produce is (mostly) good, and the selection is by far the best in Philly's Chinatown. If you want a specific type of soy sauce or chili sauce or bok choy, this is the place to get it.
Great store especially if you're looking for Caribbean products. It seems generally aimed at a Hispanic population with its vast array of Latin American food, but it also knows it's near some pretty yuppie/hippie neighborhoods, and carries things like soy yogurt and organic granola and a pretty good selection of vegetarian options. They also have some ethnic products from Mexico, Indian, and Middle Eastern that are harder to find elsewhere.
This Indian grocery store had the best selection and service in the University City area. This is the place to get Indian groceries in Philadelphia. They've got such a tremendous selection of legumes, condiments, chaat mixes, nuts and fruits, I find things here that I can find nowhere else in the city. If you adore Ethiopian injeeras, you can get a nice sack of them to keep you full for days.
Dana Mandi is a great spot to know about in University City. First the store itself is loaded with food stuffs from the Indian sub-continent. Lot of indian groceries are available. Do try out!
This grocery store stocks Indian & South Asian staples, specialty foods & convenience items. One of the the cleanest and most well-stocked South Asian grocery stores in Philly.