Flight schedule on July 1, 2016: Almeria - Madrid - JFK - Cleveland (Madrid to Cleveland was on American, booked through Iberia)
Arrived JFK at the AA gate to find that the onward flight to Cleveland had been delayed. There were never any announcements to this effect, and the indicator board (which carried several flight details) didn't show anything concrete until the flight was cancelled due to a major storm. At that point, there was no assistance from any AA personnel, and it appeared that the more the queue for customer service grew, the fewer agents there were: they left their desks one by one, not to be replaced.
A kind fellow passenger allowed me to use her cell phone to call AA Customer Service to rebook my flight. The earliest available flight was in two days' time, which would have put me in Cleveland a day late for my intended event. There was no assistance for an hotel for the night: I had to use booking.com to make my own reservation.
I cancelled the revised reservation and took a Greyhound bus from NYC to Cleveland in order to get me to my destination on time. I claimed a refund from AA for the unused portion of my journey and after THREE MONTHS was told that I had to claim from Iberia. I am still waiting for my refund and Iberia is being unhelpful to the point of being obstructive.
AA Customer Service in JFK is diabolical to the point that I will not book an outward flight via that airport again. I'm not keen to use it on return journeys, but sometimes there's little option to get back to Europe unless you want a journey that lasts for 2 days.