Ooooh! I like this topic. Here's my personal opinions of all those companies and a few more:
GE - Used to be great, but recently they seem to be focusing more on their nuclear reactors and jet engines than their home appliances - understandably so, there is a much higher profit margin to be had there. This focus shift has left them in a bit of a gray area, where i feel as though you can usually get better products from their competitors. That's not to say they don't have their high points - they have the most econimcal top load washer out there - a 4.1 cu. ft. HE unit for around $500. Ashame then, that it just doesn't feel as sturdy as the similar models from its competitors.
Kenmore - The fake appliance brand. They don't make anything themselves, but somehow they still manage to come up with some unique exclusive features and offer pretty much everything out there, for less than their competitors. Strange that you can look at a Kenmore item side by side with its Whirlpool or Frigidaire counterpart (whoever actually made the item) and somehow the Kenmore is less money, and usually tacks on one extra feature. No wonder its the number one appliance brand in america.
Whirlpool - My personal favorite brand. They make every kind of appliance out there, and most of them are manufacturered in the States. They've been around forever, and know what they're doing. I've always had lots of luck with Whirlpool and Whirlpool-Made appliances lasting a long time with little or no repair work, and all my friends, family, and most of my customers seem to agree. They don't offer a lot in terms of top-end appliances these days, only having a few Whirlpool Gold items, but they do own plenty of other brands in that market segment to make up for it. (Maytag, Jenn-Air, KitchenAid)
Maytag - They invented the modern washing machine a hundred years ago, and have survived because of their ability and expertise with them. They went on a downward spiral about a decade ago, with a lot of poor design choices that caused them too loose some customers. Then Whirlpool swooped in to pick them up and turn them around, and now they are a top company again - using mostly directly copied Whirlpool designs, but testing all their components to twice the standard as other manufacturers do. That means that you get basically the same thing as a Whirlpool, with a bit of a price premium, for what should last twice as long - but they don't back it up with a better warranty, unfortunately.
Jenn-Air - Probably the most prestigious American company Sears sells. They are all very elegently styled and feature full, and come with a price tag to match. If you can afford them, they are bound to last a long time and provide you with lots of luxorious features. (But, generally, you can find a lot of similar features with a slightly less stylish design from another company for a lot less.) Jenn-Air specializes in cooking and ventilation, but also makes refrigerators as well.
KitchenAid - Somewhere between Jenn-Air and Maytag, these appliances range from the middle to just shy of the very top end, offering generally more features than most companies, and slightly more thought out styling, without quite hitting the price point of Jenn-Air. Usually, KitchenAid is one of the most economical ways to get a well styled convection oven with just a few of the bells and whistles you want. (This brand is pretty exclusive to kitchen appliances, and make a line of small appliances to match their major appliances, a nice touch.)
Admiral / Roper / Ingles - Sort of like Kenmore, these are applianecs sold at large retailers as their own store exclusive brand. They are all made by Whirlpool, and sold only at Home Depot, Lowe's, and Best Buy respectively. Generally, they fall into the lower and mid range markets, making units appealing to those who are most budget conscious - they are essentially the same as a Whirlpool, except usually sold for a bit less. Being made by Whirlpool, all these are solid choices for someone who is shopping at the respective store and wants to save a few bucks over the Whirlpool.
Amana - This seems to be Whirlpool's answer to stores who are not large enough to get their own exclusive brand name. Amana, like the brands above, is manufactured by Whirlpool with the budget conscious in mind. Stores that have their own brand often don't floor these items, as they are in basically the same market - but you'll find them in most mom and pop stores, making a nice line of similar to whirlpool products for a bit less, most of the time. Amana is usually marketed a lot like Kenmore - they show off that they are either giving you more features for the price, or simply less money for an identical item. Again, being built by Whirlpool i feel as though these are good choices. A lot of times you can get a slightly more elegant Amana for a better price than a less eye appealing Whirlpool item, if that's the case - go for it!
Frigidaire - Another of the longest standing American appliance companies, they are now owned by Electrolux of Sweden. Still mostly made state side (or in canada and mexico) they got famous on their fridges, and now make everything out there - some of their freestanding ranges stick out in my mind of having some really cool features. While i usually direct people to Whirlpool brands for most items, i do love the features Frigidaire puts into its freestanding ranges - particularly that oval fifth burner for gas stoves. Good build quality and very reasonable prices make them a solid buy.
Electrolux - Oooh, Shiny! Great machines, but with a price tag that most people will run away from at top speed. They have a few exclusive features that are very cool, and undoubedtly make some of the most stylish appliances i have ever seen, but since they set the prices of their products for retailers, there's no reason to shop around for a sale, because there wont be one - and chances are, you can catch a competitors similar product for less.
Tappan / Estate / Brown / Galaxy / Hotpoint - A bunch of brands i didn't feel like talking about seperately, because even thought they are owned by different companies, they all are basically the same thing - the cheapest products out there. They are also the main brands for apartment sized appliances. Not necessarily poorly built or a bad brand in general, they just market themselves in a position for people who dont need extra features or want to spend as little as possible.
LG - Life's Good! I forget what other company merged to form LG, but i do know the G originally stood for Goldstar, a company with a pretty long history of making appliances. Now backed by the South Korean government, they've been able to aggresively develop and market lots of products in a fairly short amount of time. They have some really cool features, and are usually styled very nicely, and with a pretty reasonable price. The only problem is they need to import everything from Korea, so repairs can sometimes take forever simply waiting for a part. I think their appliances are super sleek and i like them for that, but being such a large conglomerate scares me a bit - I prefer companies that specialize on a certain type of product, personally.
Samsung - Similar to LG, Samsung is another Korean Government backed conglomerate, having also recently gotten into selling appliances stateside. Usually they have very nice styling, but price wise they are usually priced similarly to Kenmore products. Considering my only exposure to Samsung has been through their electronics - all of which broke in a hurry, even their high end products, i'm not very inclined to buy from them. (And, they have the same problem as LG as far as part shortages.)
Bosch - A great mid to high-end German company. Yes, they make Spark Plugs. They've also been making appliances for quite a while, and tend to have very unique designs that both look and function well, albeit a bit different than you may be used to. Bosch is the only company Sears carries that backs up their claim of better engineering with a 2 year warranty, instead of the 1 everyone else offers. A lot of people seem to think that Bosch are pricey - while they do offer some very high end and equally high priced appliances, they are competitively priced against other appliances that match the bells and whistles they have. They often compete more with Kenmore Elite, Maytag, and Jenn-Air, and it shows in the features they tend to have standard.
I could blabble about appliance brands all day, it seems!