I've kept my US credit and debit cards, even though I've been here for going on ten years now. It's useful for me because:
1. Both cards are with the same credit union that the rest of my family banks with, so they can transfer money into my account and I can withdraw it at any cash machine here
2. The APR on my US credit card is 9%-something, as opposed to my Barclaycard (Platinum), which is 20%-something. This makes a huge difference on large purchases.
3. They don't use the crappy "Verified by Visa" system in the US so I like to use my US debit card for online purchases to avoid all that BS
Like Mrs R, I initially had problems putting my UK address onto my US account, so I had to ring up to let a customer service person add it manually to my account. No biggie, and I receive my statements, letters, and cards fine (though most of my statements are pdfs these days).