In my experience this seems to be much less of a problem now with contactless payments, in both directions. US cards that used to require swipe-and-signature or chip-and-signature instead of chip-and-PIN seem to just work in when tapping (at least in the 3-4 countries I’ve traveled in extensively, although contactless isn’t widely accepted in some countries) and cards from a few European countries seem to work with contactless which is finally increasingly widely adopted in the US.
Back around 2008, I recall having problems because my Australian cards would be prompted for a 5-digit zip code. It only happened at gas stations for some reason. The closest we have is 4-digit postcodes, which it wouldn't accept. Eventually, I figured out I could prepend a 0, but I didn't want to trial-and-error that unless it set off a fraud flag with my bank. Probably a good thing it was pre-pay in the cases that didn't work.