I'm in the same camp as the people who want to be left alone when shopping, and just want a competent response to questions or problems.
Sky TV were awful, and whenever I called them over a period of about 3 years I'd get either useless incompetence or snarky arguments about how problems weren't their fault. They were just terrible, and even when I went to finally dump them for good it took 20 minutes while they desperately tried to make me stay with them. (Search my posts for "sky" for some good rants - haha.)
We've had Plusnet for broadband & phone for about 4 months, and have thus far been mostly happy with them. We had a problem where our line speed dropped dramatically and there was a ton of noise on the line, and they were eventually able to resolve it. It took longer than I'd have liked, but some of that was waiting to see if their efforts were working, and their customer service people were always friendly and helpful on the phone.
I've had an Orange cell phone since arriving in the UK in 2007, and they've always been nice and helpful both in the store and on the phone.
Amazon is excellent. I can buy from the UK or US site, using a US or UK account, and have my purchase sent to a UK or US address. They're the only company on Earth (that I know of) that doesn't care where I live, where I'm paying from, and where I want my item sent. They just take my money and do what I tell them and that's really all I'm looking for.
As jayvee said, the utility companies baffle me. We moved into our new place in October 2010, initiated a change of gas/electricity supplier immediately, and the process just finished last week. 90 days to switch from one to another is utter madness. I contrast this with getting electricity put in my name in an apartment in New York City, which took one phone call that lasted 3 minutes.
I get the feeling that in the UK, some of the older companies that used to enjoy a monopoly (gas, power and phone, mostly) and didn't have to try to make customers happy are not as attuned to their customer-facing requirements in the 21st century.