Giant - General groceries, many locations.
Harries Teeter - higher end products and many locations.
Whole Foods - the same that says it all. There are fewer locations in Northern Virginia, but you can find Whole Foods stores in Clarendon, McLean, Fairfax, and Springfield.
Trader Joe's - a lower priced counterpart to Whole Foods, Trader Joe's offers more in the realm of whole and organic food products at reasonable prices. There are just a few locations, but they make up for it in size.
Safeway - this is a national chain, that many people are familiar with. You do still need your Safeway card for the good pricing!
Wegmans - a fun and exciting way to go shopping, Wegmans, only a handful of locations is an epicurean market kicked into high gear. It reminds me of the Central Market platform with a wonderful produce and dairy section and gourmet options for deli, and pastry. You can even grab a meal at the Wegmans while you're there. The closest Wegmans to NOVA is in Fairfax, VA. Another location is slated for 2012 in Arlington.