Most US credit cards do not have PINs that can be used for purchases - only for cash advances. I heard one story of someone who tried to do that - use the credit card's "cash advan e PIN" - to make a purchase, and it was charged as a cash advance!! (That is, with immediate interest charged, very expensive).
So personally, I would never try to use a PIN for a purchase in Europe unless your credit is EXPLICITLY a "chip and PIN" credit card. If the credit card company doesn't offer you a PIN by default, assume it's not "chip and PIN" - just "chip and signature."
There are a few very "chip and PIN" credit cards available in the US. I do have one. On my last trip to Italy in May, I had a couple of "chip and signature" cards (better benefits) as well as my "chip and PIN" card - but I never needed the chip and PIN card this trip. I used the chip and signature card everywhere, even at a Trenitalia ticket machine (no PIN required - your mileage may vary, as they say). For small amounts, your US chip and signature cards may be accepted at machines without a PIN. Mine have been numerous times in different countries. I've only rarely needed the chip and PIN card (e.g. in Amsterdam at train ticket machines).
When making a purchase with a US card that is just "chip and signature" when a human vendor is involved - at a store, restaurant, hotel, etc. - they will automatically get a printed slip for you to sign, instead of being asked for a PIN like Europeans do. Most businesses who deal with tourists are aware of this, but occasionally you'll find a clerk who isn't used to dealing with a credit card with no PIN and may not even realize you have to sign the slip.