Here are the accounts that I know of that charge no fees for making purchases / withdrawing cash in the US:
Citibank UK - as mentioned in a previous post, the combined citibank current/USD current accounts for expats in the UK are a great way for expats to use their hard earned £'s in the US. The accounts are fee-free, and they're also very basic. There are fees involved if you want an overdraft, but for someone who wants to transfer some money over to spend whilst in the US, you couldn't do much better, except for...
Santander Zero - this current account is only available for Santander mortgage holders, and like the name says there are zero fees involved, including when using your debit card in the US. They may open this up to the wider public, at which point I'll be there like a flash.
Santander Zero Credit Card - as above, this is a great card to use worldwide as there are 0% loading charges. I have had difficulty getting one of these though, so I assume you have to have great credit. This card also uniquely allows you to withdraw cash fee-free worldwide, but you get charged interest immediately as you do when you get cash advances on credit cards.
Nationwide FlexAccount - this is a great current account that charges 0% in Europe and 1% everywhere else. If you're not that fussed about the 1%, this is a great and easy to get account.
Nationwide Credit Card - as above, it charges 0% in Europe and 1% everywhere else. I have never tried, but I think it may be easier to get than the Santander Zero card.
Post Office Credit Card - like the Santander card it charges 0% worldwide, but I have found it difficult to get one, and is a total pain to go through the application process.
Some other points:
I have found that PNC does not charge fees when using UK debit cards to withdraw money at one of its branches in the US.
You may be able to use your Barclays debit card fee-free at Bank of America as part of the Global ATM Alliance, but I have not tried this.