Many US cards still don't work. It is still a problem. Others just aren't accepted everywhere even if they technically would work (same problem you might have in NYC or other American cities). Still others should work but don't, and even the store or restaurant in question doesn't know why.

Most places accept credit cards (though not all). The question is whether yours will work. The answer in my experience is that you have about a 30% chance, on average, with any given card. Some cards are more reliable than others, though.

I can say that my Chase cards worked maybe once out of the 20 times I attempted to use them last November, and I doubt much has changed since then. It was really disappointing because those are the cards I have that charge no foreign transaction fees. They only worked at Narita airport.

Luckily on that trip I made sure to carry three different credit cards and always knew where a 7-11 was. So I didn't have any real problems. AMEX is the most reliable card, Citibank is probably #2 (though it's not foolproof), but many times I did have to use cash.