I generally use a car service when arriving at JFK. There are many of them to choose from and their fares usually are from $30 - $35 (without tolls and tip), not very different from the taxis. At night, the taxi pickup area at some terminals (such as 7) is absolute bedlam. I typically reserve the car in advance and then call the 800 number when I arrive. I am given a car number to look for and they usually materialize about five minutes later. Over the last few months, I have been using Tel Aviv Limo (212) 777-7777, 1 (800) 222-9888 and don't have any complaints.

If you don't want to spend much money and don't mind a long uncomfortable ride via the "scenic" route (and I use this term very loosely), you could take the free bus to the last stop in long term parking and then grab the subway at the Howard beach station. You'd get there eventually

As a compromise, there is also a company that offers shared rides; you can inquire about them in the baggage claim area. You might be able to save about $15 or so, but the length of your trip would increase quite a bit, especially during rush hour or on a Sunday night.