In the general San Diego area (this is purely off the top of my head):
-Ralphs and Food 4 Less (Grouped together as they are Kroger subsidiaries.)
-Albertsons
-Vons
-Trader Joe’s
-Costco
-Henry’s Marketplace
-Stater Bros. (I think this is entirely a local chain.)
-Whole Foods Markets (Just two in the area I can think of.)
Star Market is actually Shaw’s. They had to keep the “Star Market” name so as not to cause a monopoly of Shaw’s all over the place.
Victory was recently bought out by Hannaford. They should be switching completely over to everything Hannaford by early summer.
What I’ve always found curious is that we’re the last area of the mainland US to be inundated with the national chains. Albertson’s acquiring Star/Shaw’s is, I think , the first (I’m not counting Stop & Shop’s parent company nor Hannaford’s because they’re both overseas conglomerates).
We don’t have any super Wally Worlds, for instance. I think there’s only one in the entire state. And to tell you the truth, I’m not sure how I’d react upon seeing an actual supermarket within a Wally World 
We do have a lot of mom-and-pop stores and smaller chains like Victory/Hannaford and Market Basket. Maybe it’s because of the smallness of New England or the vast physical distance between us and the rest of the country, I don’t know.
I know I’m being nitpicky, but I’ve been in this business for a long time, and obviously I like talking shop 
In the Seattle area Fred Meyer, Safeway, and Albertson’s are the big 3. We also have QFC, Top Foods, Winco, and Thriftway. There area couple Trader Joes (both very small for a grocery store), Larry’s Markets (excellent meat department), a few SuperWalmarts, Uwajimaya (local Asian chain), and Red Apple.
We have the usual, Farm (next to the Jareer Bookstore) Danube and Sawary Super Store (best for baked goods). We used to have a Safeway affiliate, but it is long gone.
Here in Richmond, Virginia, we have tons of Kroger stores, tons of Food Lion stores, a lot of Ukrops (local chain). I have a Winn-Dixie across the street from my sub-division, but they are going out of business.
When I first moved to Richmond, we had Farmer Jacks, The Grocery Store, Safeway, Hannafords. They’ve all gone out of business in Richmond.
Eric
When I lived in NYC I shopped for big grocery runs at Waldbaum’s, Pathmark, A&P and ShopRite. Waldbaum’s was good for prepared foods but rather expensive for basic items. The ShopRite lost points for bad spelling but had great selection and good prices.
In the Tampa (OK, Brandon, to be specific) area we have Publix (where I work on the weekends), Winn-Dixie, Kash n Karry, Albertson’s, Target, and Super Wal Mart. We used to have Food Lion and Thriftway, but they have gone by the wayside.
The Albertson’s in our area are being transformed into something called SuperSaver; it’s going to compete with Super Wal Mart.
Publix is headquarted in Lakeland , which is not that far from here. Most people shop Publix.
In Greensboro, NC, we have Harris Teeter (the most common by far), Bi-Lo, and Food Lion. There is the occasional Winn-Dixie and a Lowe’s Foods hidden somewhere. We also have two Fresh Markets (a small chain of “specialty” grocers) and all your basic Uber-Marts.
It was weird coming from Lexington, KY, where (as brianjedi points out) you can’t take a whiz without splattering some on a Kroger, to a town that is entirely Kroger-free.
Hmmm… If Albertson’s has bought Acme, then if the outfit that markets the Roadrunner high-speed ISP buys Albertson’s – what will poor Wile E. Coyote do? :smack:
The ones I’ve been in have a grocery side and a regular Wal-Mart side. They’re really big stores, generally open twenty-four hours a day. So you can do your shopping anytime. My best friend moved from Pennsylvania to Texas and told me of her astonishment upon entering her first Super Wal-Mart. She is enamored of the “24 hour” concept.
Up in Schenectady, there are Price Chopper and Hannaford. There are also SaveRite and Save-A-lot – smaller stores with cheap items and knockoffs (great prices, if dare eat what they have). The other chains – Grand Union, ShopRite, Great American, Albany Pubic Market, A&P, P&C – are either bankrupt or pulled out of the area.
When I was growing up on eastern Long Island, the big store was Bohack’s and A&P.
Here in my section of Michigan, we have the following stores,
D&W
Villiage Market(or village idiot)
Super Wal-Mart
Meijer’s
Martin’s
Sav-a-Lot
Aldis
Hardings
and I think thats about it.
The only thing that really matters about the Boston Metro area supermarket situation is that we don’t have a Wegmans. 
But in addition to Shaw’s/Star, Stop&Shop & ones that others have mentioned, we also have Johhnie’s Foodmaster. Some Johnnie’s are kinda crappy, some are good, none are luxurious. The one near my house is one of the good ones. Selection is mediocre, but the prices are good & the staff are very nice.
Toronto. The local ones are an IGA and a Valu-Mart, both of which are expensive, poorly stocked, and small. A little farther away there are a couple of Loblaws (medium range to gourmet pretensions) and a No Frills (cheap but a lot of the same brands as more expensive stores). There’s also a Price Chopper and a Dominion. Oh, and a Sobey’s. All within about a ten-minute drive.
I personally shop at No Frills, Loblaws, Bulk Barn, some big Asian grocery store whose name I forget, CostCo, Nasr (big Middle Eastern supermarket), and the St. Laurence Market (huge multi-vendor indoor market). We have a Whole Foods here but I try to avoid going near it because I am not safe in fun gourmet grocery stores.
As I have said before, I would kill for a Trader Joe’s.
Cleveland, Ohio - Giant Eagle, based out of Pittsburgh, is considered the more upscale supermarket, followed by Heinen’s (a local chain) and Tops (a chain from Buffalo). Marc’s is a very low-end discount grocery store chain. (The Marc’s near my house doesn’t even accept debit cards.) Dave’s is another local chain, found mostly in inner city areas.
Buffalo, New York is dominated by two chains. Tops (local headquarters, but owned by Royal Dutch Ahold) has the largest presence; their Buffalo stores are much larger than those in Cleveland; usually 80,000 to 100,000 square feet or so. Tops stores are found throughout upstate New York, northeast Ohio, and in some southeastern Asian countries.
The other biggie is Wegmans. Take a regular supermarket, put it into a Whole Foods-like setting, add exotic and yupscale products to the mix, and multiply the size by four, and a Buffalo-area Weggies is the result. There’s really nothing that compares anywhere; Wegmans are truly magnificent stores.
The biggest Wegmans in Buffalo, on Maple Road by Boulevard Mall, is across the street from the enormous Tops International store. They’re both tourist attractions; they attract busloads of shoppers from Canada.
There’s a Greatland Target (aka Super Target) in the old Montgomery Ward builing in Seven Corners.
I completely forgot about Foodmaster. And Roche Bros. :smack:
And yeah, it’d be nice to have a Wegman’s around…
Southern California, Inland Empire
Albertson’s
**Von’s **
**Stater Bros. ** (The original store is in my town.)
**Lucky’s ** (Many stores bought by Albertson’s)
Trader Joe’s
Safeway
Wal-Mart Superstore
**Food-4-Less ** (A you-bag-it place)
We tend to shop a few local markets, like Gerrard’s and Annette’s. Slightly pricier, but better selection at the deli counter and wonderful beer and booze aisles!
Oddly enough, Harlem has one of (if not the) the best supermarkets in NYC, the glorious Fairway on 12th Avenue near 125th, underneath the Riverside Drive viaduct. It’s a great market – you could spend an hour in the cold room alone – and it has a (rare in these parts) actual parking lot. With an expensive river view! Besides that, 'round these parts it’s mostly places like the the (usually grim) C-Town, which I’ve found to be as reliable an indicator of a down-at-the-heels neighborhood as bail bondsmen and check-cashing places.
I can see the Whole Foods Market in Edgewater NJ from my window, but it’s across a river and not that convenient (until it freezes over). Whole Foods’ are also usually filled with the kind of people who make me want to take up smoking and barbecuing dolphins (although my hunch is that it’s a great pickup joint).
Huge Shop Rite in Englewood, New Jersey. Has everything in the world in it, including a coffee machine and a bathroom. And it’s open 24 hours. I wish they would let me live there.