I have chip and signature rather than chip and pen.
Has anyone experienced problems with these cards?
Sure. They are not the same and will not work where a chip and pin card is required. But will work anywhere the mag strip card is accepted.
We had no problem using it (Bank of America) in stores, car rental or with a person at the train station but ticket machines, gas pumps and toll booths were another story. It was hit or miss, sometimes it worked, sometimes not.
To avoid confusion, I am guessing you mean chip and "pin", i.e. personal identification number. It doesn't hurt to have a PIN on an old-fashioned swipe-strip card, either.
Some unattended machines it will work, since each one may set a low amount where a signature or PIN is not required for the transaction, ie buying a tram ticket in Zurich. Others, ie vaporetto tickets in Venice or Italian train ticket machines, require a PIN. Chip & PIN is the way to go, as it covers everything.
Last summer I had both a chip-and-PIN and a chip-and-signature card in France. The chip-and-signature worked if there were attendants and at the Paris Metro ticket machines. The chip-and-signature card did NOT work at French train station machines and automated gas pumps. The chip-and-PIN card worked at these automated machines. The autoroute was another story. Depending on the company managing the autoroute, NO card would work in the toll machines. I always made sure I had enough cash and used the cash lanes. Usually the machines that take cash also have a slot for a credit card, so I could try it first to see if it would work (it often didn't).
Some machines that want a PIN for purchases have worked with my (chipless) Visa Debit/ATM card and PIN, such as for RER tickets at CDG airport or train tickets in Italy. As mentioned, you can request PINs for your credit cards, too, before leaving home. (But don't use a credit card to withdraw cash from an ATM, as interest starts to accrue immediately for those cash advances.) It's always good to keep plenty of cash on hand, since many smaller businesses prefer cash and some ticket machines will also take either coins or bills or both.