I am arriving at JFK on an internatioal flight and ticketed to connect to another doestic flight. I now wish to spend a few days in NYC. I realize I will have to collect my bags and go through customs. Can I leave with them and not get on the connecting flight?
Thanks.

Welcome to flyertalk!^

Yes, you can leave with them.

If you plan on using the rest of your ticket, you will want to read the airline's CoC and the fare rules of your ticket; most carriers will invalidate a ticket and cancel a reservation in the case of a no-show requiring a new ticket to be bought, perhaps using the invalidated ticket as a credit.

But if your experience is the same as mine, you WILL end up arguing with a TSA person stationed at the exit of the baggage recheck area (depending on terminal) about being allowed to take the bag through.

If you decide to do this, take the baggage tag off at the earliest opportunity, and before you get to the recheck area.

I had a hassle with this at both JFK and ATL with a legal-sized carry-on that was checked from London->US during the UK's obnoxious one-personal-item rule period. By hassle, I mean the TSA folks sent me back to the recheck counter when they saw the tags, and DL personnel didn't want to let me take the bag carryon. They had to cancel it out in the system before they'd let me go, and then they had to speak with the TSA folks to tell them what they did. By the time I was done with those clowns (TSA and DL), I had missed the earlier connection that I could otherwise have made.

Alternatively, ask the gate agent at the departing airport to check your bag through to JFK and not your final destination.

Once you get the bags off the belt and go through Customs, wouldn't you just head for the exit rather than the baggage recheck area? Grab a cart and place the bags so tags are face down or hidden from view.

If the skipped segment is the last flight on this ticket, that's all you'd lose out on. But as Ari said, if you have onward flights after that one, they'd be cancelled out. If you still need to get from NYC to your final destination, you might be better off to pay any change fee and just change the date to allow you a few days in NYC, rather than buy a new one-way ticket.