Here's an example of what you're describing: BikeTrailorShop.com

This online business is based here in Flagstaff, Arizona, where they manufacture their own "Wandertec" utility bicycle trailers, seen here: http://www.biketrailershop.com/wandertec-trailers-c-283.html

At the same time, they sell a number of other utility trailers, including BOB, Burley, Carry Freedom and more, which you'll see in the left-hand column of the above website.

This business, now selling world-wide, began with just their own brand, manufactured in the founder's garage (down the street from me), but eventually branched out to sell bike trailers and related products by other manufacturers. It was that move that really catapulted their business to a new level, and now they occupy a downtown location with a 4000-square-foot warehouse and do millions of dollars in business.

Kirkland Signature is Costco's store brand, otherwise known in the retail industry as an "own-brand," "house brand" or "private label." It is found exclusively at Costco's website and Costco warehouses and is trademarked by the company. The name derives from the fact that Costco's corporate headquarters was located in the city of Kirkland, Washington between 1987 and 1996.

I bring this one up specifically because Costco has apparently done surprisginly well with this brand, many marketers would cite the overall shift in consumer buying habits of being more thrifty, but Costco has had a much greater success with their personal brand than many others apparently.

They of course sell many other brands that compete directly with the variety of products that the Kirkland Signature brand offers.

You will actually find this trend in a lot of grocery stores and drug stores obviously as well, as many sell their own "generic" brand to appeal to the cost-minded customer.

As for internet businesses, I can't think of another one that is as good as an example (or indeed an example at all) like Amazon, as even most large internet "stores" such as Zappos do not yet offer their own products, many serve simply as a place to purchase other brands with the convenience of online, but with Amazon's massive size, it seems they are probably the most successful in the selling of their own products (which to be honest they probably outsource to some other company haha)

If you are mostly looking at internet businesses, here are a few that you can take a look at:

The iStore sells apps that were created by both Apple, and other companies. In many cases, these companies have apps that are almost identical to those created by Apple and it's subsidiaries.

The Playstation Network by Sony sells games and downloads for the PS3 and PSP. Most of the games, apps, and extras were not created by them, but by other companies.

Chaosium.com, which is the home of the company that makes the Call of Cthulhu role playing game sells other products from time to time from other companies. Usually, you can find novels that are along the same lines as the novels that Chaosium publishes for fans of the game.

If you are looking outside of internet-only, there are more examples:

Target, Walmart, Costco, CVS, Macy's, and JC Penny all have their own lines. They sell them on the same shelf as the competitors. This has been a staple in the retail community for many years.

Trader Joe's, a high-end grocery chain, brands almost everything under their own name or some variation of it (like Trader Giotto's for Italian products. But they do have some name brands, especially in the wines.

Here, from their website, is a list of favorite products for 2010:
http://traderjoes.com/pdf/attachments/traderjoes-2010-favorite-products.pdf

The "Charles Shaw Wines" are their famed "Three Buck Chuck" which are apparently very good and incredibly inexpensive. You can even see "Joe Joe's" and "Frozen Joes" on the list.

Aldi Supermarkets, a discount store with no frills, does the same for their items--they have some house brands but also sell name-brand items.

It's no surprise--I'd heard that the two chains were started separately by two brothers.

Seconds ago, in researching this answer to give it street cred, I read their story:

"Theo Albrecht died recently. You don’t know his name, but you know what he’s done. He was one of two brothers who created Aldi in West Germany after WW2, and was instrumental in its European and later worldwide expansion. The Albrecht brothers had a disagreement in the 1960s over selling cigarettes, so they split Aldi geographically in Germany, with Theo running Aldi Nord. In 1979, a family trust of which Theo was a member bought – and still owns – Trader Joe’s. And if you think about it, Trader Joe’s is Aldi with better frozen foods, higher quality groceries, and a cute concept."

Source: http://wnymedia.net/buffalopundit/2010/08/the-aldi-trader-joes-connection/

You should note, that what may appear to be competition may not actually be. Custom-branding is the term you want--the manufacturer takes their product and will basically stick any name and design on it for a fee.

I tried to do an internet startup of a niche-market gourmet food and found that a lot of what I may be buying as produced at a particular farm stand's store wasn't from that farm. It was custom-labeled. Explains how a farm in The Midwest call sell its own brand of farm-fresh Orange Marmalade..

How about EXACTLY THE SAME products under different names, one brand-name and one store-brand?

For example, I once read that Vi-Jon Labs, right here near me in Saint Louis, Missouri manufacturers some outrageously high percentage like 80%+ of the alcohol-based hand sanitizer on the market today.

At first I thought it was ridiculous--not only is there their own Germ-X, but there are dozens of drug chains and grocery stores that have their own brands. (And maybe even something like a "Trader Anti-bio")

Read the labels, though--Aldi, Trader Joe, supermarket, pharmacy chain...it all says "MANUFACTURED FOR..." They don't make any of the stuff themselves.

Then take a look at Vi-Jon's website and it's obvious: Any of these bottles look familiar to you from your local Health & Beauty Aids aisle?

http://vijon.com/images/swan.jpg

Likely so. Read Vi-Jon's Private labeling info:

"Vi-Jon, Inc. is one of the nation’s oldest Private Label Health & Beauty Care Companies, serving retailers in all 50 states. Vi-Jon operates manufacturing and distribution centers in Missouri and Tennessee around the clock to distribute our products across the nation. Vi-Jon headquarters has called St. Louis home since 1912."

"For over 100 years, the Vi-Jon name has come to represent one of the highest standards in the manufacturing of quality products in the Health and Beauty Care industry. Vi-Jon works closely with every customer to provide a combination of quality and value for the consumer and the retailer, while our commitment to innovation and technology ensures that our products meet or exceed our customer’s needs."

Then, there's a link a page:"Vi-Jon's Products."

"Our private label products are tested and graded by independent laboratories for characteristics including: appearance, fragrance, packaging, and performance. This independent testing assures retailers that the products that they buy for their own Corporate Brand Programs are truly safe and effective.

"List of Private Label Products

* After Shaves
* Baby Care
* Body Wash
* Dental Rinse
* Deodorants
* Hand Sanitizer
* Light Body Oil
* Antibacterial Liquid Soap

* Lotions
* Medicated Chest Rub
* Mouthwash
* Nail Polish Remover
* Petroleum Jelly
* Shampoo/Conditioners
* Shower Powder

"Vi-Jon Laboratories progressive Private Label product offerings remain current as national brand companies continually re-introduce their products with new sizes, fragrances and packaging. We work closely with our customers to make certain that we continue to offer the right combination of value to the consumer and to the retailer."

So for a fee, I can have Gary Allen After-Shave, complete with my picture & autograph

Vi-Jon is just the tip of the iceberg. Think about it--drug stores don't produce things--it's not possible for them to manufacture thousands of items of every kind with their own name. Grocery chains aren't canning their own jelly & vegetables. (Or making shampoo or hand-sanoitizer.) They just sell them.

They're just selling the product at their stores..

For hard goods, here are three examples. Many years ago, I used to sell household appliances to the property management industry.

9 times out of ten, for rental properties, I was selling:
-Hotpoint by General Electric
-Roper by Whirlpool
-Magic Chef by Maytag.

The former is the lower-priced version of the latter--but go to a Home Depot or Lowe's and you'll see that except for the name and maybe a feature, the former is exactly the same as the latter--it's a different name sticker. A 15 cu. ft. fridge is a 15-cu. ft. fridge.

If I remember correctly, Whirlpool manufactures most of the stackable laundry, no matter whose name is on it.

Take a look at these stackables. Whirlpool:
http://static.howstuffworks.com/gif/productImages/9/5/00000119395-WhirlpoolTopLoadStackedWasherDryerLTE5243D-large.jpeg

GE:
http://images04.olx.com/ui/1/14/41/14161341_1.jpg

Frigidaire:
http://www.stackablewasher.org/wp-content/uploads/2010/06/fregidaire-300x300.jpg

Maytag:
http://i.ehow.com/images/a07/87/16/maytag-stackable-washer-troubleshooting-200X200.jpg

Kenmore (No such manufacturer--it's just the Sears brand)
http://iwonder-all-categories.3025048.n2.nabble.com/file/n3214669/00000101870-Kenmore27InchStackedWasherElectricDryer94702-large.jpeg

Completely identical.

Watch for the Gary Allen Lotions line at a store near you...?!? Could happen but won't.

In terms of grocery branding the practice of selling own brand products alongside big brand competitors is more more prevalent in the UK than it is in the United States.

This is for a number of reasons. The breadth of brand choice is greater in the US than it is in the UK to the detriment of own brand products. Stores such as Tesco (mother ship of Fresh and Easy in the US) is one of the biggest retailers in Europe. They also have a massive online business that sells everything from baked Beans to financial products like mortgages. Tesco has a sophisticated own brand marketing strategy that caters to all price points. There is a no frills economy line called Basics that has minimal graphics and at the other end of the scale there is a finest range that caters to an altogether more upmarket clientele.

Interestingly other British retailers such as Sainsbury ape this very successful business strategy with their own versions. At the higher end of the retailing scale premium brand retailer Waitrose which is part of the John Lewis group also carries own brand products alongside other products but the focus her is very much on the own brand product rather than the type of FMCG that other big box retailers stock. It would Seem that TV advertised is OK her but only in moderation as it ‘brings down the tone’ Of course perceived value is very important to higher end retailers such as Waitrose and their very effective strategy has seen them expand their business dramatically throughout the UK in recent years.

Boots the chemist is the UK’s leading drugstore. They have a long tradition of stocking their range of highly successful own brand products prominently alongside big name competitors. There appears to be no equivalent practice amongst leading US druggists many of whom give priority to a vast ocean of branded products. In a market where price conscious consumers are looking for clear visual cues to product many US retailers would do well to follow the example of the leading UK retailers