Flying to Bangkok with a change of airport in Tokyo (Narita to Haneda). Does my check-in baggage go to the final destination or do I have to recheck them in again? It's booked as one ticket flying from JFK.
I'm not aware of any cases where luggage can be through-checked between different airports, anywhere in the world. When changing between airports like this, you have to take your bags with you. (eg this BA page on London Heathrow to Gatwick or City connections clearly explains you have to collect and move your own bags)
So, on arrival at your first airport in Japan, collect your bags, and clear customs with you. Take the bags with you as your cross Tokyo. Then, check the bags in at the other airport. See this existing question we have on how to get yourself between the two Tokyo airports
It's possible that your bags may be tagged to the final destination, which saves time at re-checking and would help if they missed the flight and had to be re-routed, but you'll need to collect them and take them with you between the two airports if all goes to plan.