Having flown worldwide for forty years, the only time I have had a ramp check was in JFK. The inspector was an older fellow who was very pleasant and apologised a number of times, that surprised me. Anyway all that was checked was the aircrew licences plus medical certificates and my two pairs of glasses, all the usual aircraft documents (not manuals) and then he was on his way.
Having heard from some colleagues that ramp checks can be a little full on, I was quite surprised how easy this inspection was, not that we had anything to hide!