Good topic. I'll start with the companies that I have had personal experience with, and don't want them to get me for another dime.
HP: had an all-in-one printer that I threw in the dumpster while still under warranty. It was the fifth refurbished one that they sent me when my new one wouldn't work after a few days. I was paying hourly employees to sit on hold with with their horrible customer service each time. When I hit machine number six, I'd had enough.
Shimano: bought the most expensive fishing reel that the company made at that time. The drag would lock up if the reel got the slightest bit damp.
Firestone: had a set of the infamous Firestone 500 tires, all had tread separation within the first 18 months (<5000 miles). Then bought a used car with a single Firestone 721 (the successor to the 500), which blew out a few months later. In 46 years of driving, that's still my only highway speed blowout.
American Express: not directly my own experience, but two of my immediate family members had fraud on their cards, and AM wouldn't back them up. My distaste for them was worsened when I owned a business and saw what their cut would need to be for me to take their cards.
State Farm insurance: my dad got his Toyota pick up rolled by a stop sign runner. SF wanted to repair it, even though it was obviously totaled. He refused, but they finally had to pay him off after they "lost" the truck (stolen from where ever they had it stored). Partly because I was young and dumb, I got burned on an insurance claim myself.
Good friend of mine called his SF agent to ask about coverage on his homeowners insurance on two occasions, no case opened, just asking if he was covered under specific situations. Then his wife lost her engagement ring, and he filed a claim. He found the ring in the yard within days of that, so canceled the claim. Despite the fact that he had only made one claim, which he canceled, SF canceled his homeowner's policy, their letter indicated that he had made three claims (the inquiries counted as claim in their system). Because he had been canceled, he was automatically shunted into the high-risk category, so it cost him many more thousands to re-insure the house.
Uhaul: don't get me started. Use them occasionally for trailers since Penske only rents trucks, but I realize that it's a big risk each time.
Continuing: I'll never buy a new car since I don't think it's a good value.
Any European car. I would love to have an e36 or e46, and I love wagons, but I don't have the extra time and income to deal with the recurrent issues that go with these vehicles. Not to say that any manufacturer is perfect. I've had three Hondas with automatic transmissions and was lucky to get rid of them before they crapped out, but I've never repaired a window regulator in any of my Japanese cars. After eight years, my 04 Ralliart wagon has even been more trouble free than any of the panthers I've owned.
Finally, Apple products. Too expensive, and I really resent their policy on power cords. EU law mandates uniformity on the phones and tablets, so all of the other manufacturers equip their devices with micro USB ports, but Apple makes more money paying the fines and selling their customers their proprietary Lightning port hardware, which, oh BTW, isn't backwards compatible.
Dishonorable mention-Hobby Lobby: I'd written them off a while ago, but this year the family that owns the company was caught importing stolen artifacts for their new museum.
