I've never had a problem with any of my credit cards (I rarely do anything that requires me to see how good their customer service is, but I haven't had complaints about any of my multitude of cards), but, for all the flack given them, I've experienced good service with American Express (with all levels, from my Blue to my Platinum). You do talk to India when you call, but the agents have always been helpful and pleasant.

From what I understand, one of the best combinations of benefits and service is the SPG card from Amex, and close behind it is the HHonors card, also from Amex. One or both of those (I can't remember) carries no annual fee, too, I believe. (Those are two Amex cards I don't have...yet.)

Other than that, I've found the other banks (Chase, BofA, Citi, etc.) more similar than different, so I don't think it matters much--choose your program and look for good bonus mile offers, I suppose. (Try the credit card section of http://www.freefrequentflyermiles.com for some tips and hints on the best bonuses.)