All supermarkets have a growing selection of plant-based foods, here are some highlights:
Whole Foods - The largest selection of plant-based meats and cheeses, along with great vegan versions of your favorite foods. It's a great place to see what's available, especially the Chandler and Mayo Blvd locations.
Trader Joe's - A variety of vegan products and many hidden gems, see here http://www.traderjoes.com/dietary-lists/vegan and here http://www.buzzfeed.com/leonoraepstein/best-vegan-products-from-trader-joes#.gpYKBZlyZ
Sprouts - Natural foods gorvery store with a good selection of vegan foods.
Lee Lee International Supermarket - The largest international market in the valley, offers many premade vegan items, cheap vegetables, and spices and sauces to make your international favorites.