Bryan -
First, you asked an interesting question, and you've already received some very competent answers, which is what you can expect from the more thoughtful members of this site. In the last year I was very involved in helping my mother select a double in-the-wall oven, and we almost replaced her 2004 GE Triton dishwasher (thanks to AW.org we didn't). I built a new home in 2003 and selected all my appliances, so here's what my two cents can offer:
First, nearly everyone we spoke to while oven shopping said the same thing - go with GE cooking unless you're going way high-end. Even some sales people who would have preferred to sell other brands told us that. Mom's last GE oven lasted 21 years and got so much use, I replaced the bake element twice due to wear and tear. We sold it on Craigslist and I presume it still in use. Mom loves her new GE ovens, and I think they we very well made, though she's had to get used to convection cooking and I don't think she's sold on it. I have a Profile smooth-top 30-inch range and I am very happy with it, though Hamburger Helper isn't very picky.... (I do cook for real from time to time however).
For dishwashing, we both have GE tall tubs, mine is a Profile also and a far cry from the Potscrubber 1200 I had prior, which I'd give some of my cherished possessions to get back. We are happy with our dishwashers but their water-misery ways makes them harder to live with at times. I think I would buy a Whirlpool product next time, or believe it or not, an old-timey standard tub GE.
For refrigeration, I would definitely buy Whirlpool. I am very happy with the one I have now, and my mother has a 1995 Kitchen Aid that's been great. My 1990 Whirlpool is still slaving away in the garage, and we get upwards of 100-degrees plus in garages all summer long here. I would NOT ever by a Frigidaire product for refrigeration. Just go to an appliance resale shop that has repairs and a junk yard in the back - one nearby me is full of 5-year old and sometimes younger Frigidaires, and from what they tell me, it's not at all uncommon. Leaky compressors that are uneconomical to repair seem to be the culprits in these premature demises.
So, in a nutshell, for me its GE cooking, and Whirlpool dishwashing and refrigeration (a Kenmore branded Whirlpool machine would be fine too). I would stay away from anything Frigidaire in my own shopping, but have one more personal point - ABSOLUTELY no imported brands.
I am very pro-American on certain things, and though I've never owned anything but a Ford, I don't have much sympathy for our auto industry. However, we are quite capable of making our own appliances, and we make a whole range of very good ones. It would be a frosty day you know where before I bring the likes of Samsung, LG, etc. into my house, heck, into my neighbor's either if I can help it. I simply feel that if we don't want the rest of the infrastructure of our U.S. economy to crumble, we need to buy our own wares whenever possible. I don't argue much if someone selects a Toyota, but nobody could convince me why they needed a Samsung or LG appliance, etc. I only wish we made more front-load washers in this country.
Good luck in whatever you choose to purchase, please let us know what you decide, and most of all, enjoy it!
Gordon