Schnucks: Products that are available vary from store to store, but I've found the basics in all stores. Schnuck's carries Udi's bread, flours, some organic/gluten-free processed soups and mixes, and a small selection of cookies and crackers. However, there are a good number of gluten-free products available online at http://schnucks.elsstore.com/search?q=gluten+free.
Wal-Mart: You can find Chex cereals, gluten-free Bisquick, Betty Crocker gluten-free cake and brownie mixes, and a few types of pastas. The Cordova/Germantown locations has a more extensive gluten-free section. I hope that the Bartlett center follows suit!
Kroger: Depending on which location you frequent, you'll be able to find the following gluten-free basics: flour, mixes, cereal.
Whole Foods at Poplar and Mendenhall: I go to Whole Foods when I am unable to find a particular item that I'm not able to find closer to home. Lately, I've found that I have to order things online because even Whole Foods doesn't have them.