Here are some of the best vegan-friendly grocery stores in the Phoenix area.

Whole Foods Market
By far, the best overall place to find vegan goods. They even have a dedicated vegan section in their deli area.
[Locations in Chandler, Tempe, Scottsdale, Phoenix, Paradise Valley, and Tucson.]

Sprouts Farmers Market
Good selection of vegan basics and healthier versions of convenience foods.
[Locations throughout the valley.]

Trader Joes
Hit and miss, but good vegan stuff. Check out their vegetarian and vegan shopping lists.
[Locations in Ahwatukee, Glendale, Mesa, Paradise Valley, Phoenix, Scottsdale, Surprise, Tempe, and Tucson.]

Fry's Marketplace
Good but incomplete selection of vegan basics, try their natural foods section first.
[Locations all over the valley.]

Lee Lee Oriental Supermarket
Great for all hard to find ethnic ingredients from all over the world. It's worth shopping here for the vegetarian finds, even with the fish smell and the giant fish/meat market.
[Locations in Peoria, Chandler, and Tucson.]

For more veg-friendly stores with herbs, health food, and more, please see:

Happy Cow [dot] net