In the US, PINs are typically only required for debit card purchases.
In the US, you typically have to sign a receipt, but cashiers don't normally check to make sure signatures match. I don't blame them, that little strip of white on the back of the card is WAY too small to actually sign. Also, even if you are able to sign successfully, it just gives a thief a signature sample to copy from. Personally, I write "SEE ID" on the back of mine, so if/when they do look, they know to ask me for proper ID before accepting the card, and I always thank them for it.
There are exceptions to the signed receipt rule, however...
1) If you're buying online, there's nothing to sign. However, you typically have to enter in the name on the card & billing address, which I believe is (or may be) at least partially verified by the card processor - if something doesn't match, your purchase may not go through.
2) If you're paying at an automated system, like a gas pump, or self-scan at the grocery store. I've noticed many of these will now ask for the billing zip code, however.
3) Purchases under a specific dollar limit - I've seen a few grocery stores where, if your purchase is under $25, you don't have to sign for it. I am guessing this is also why I've never been asked to sign a receipt on one of the few occasions when I have used a CC at a fast-food restaurant.