LarryU's correct on the car service angle. I have used just about every NYC car service and like Larry, right now I'm using TelAviv. I've been picked up in everything from a brand new Lincoln to a beat up old one--you never know. But either way there's much more room than in yellow taxis--some of which can hvae the driver's barrier so far back you'll swear your in coach on a charter flight.
CAR SERVICE TIP: when you make your reservation, tell them you want to pay cash--even if you want to pay with credit later.
The reason: Let's say three people arrive at JFK at the same time. They all have Tel Avivs booked: #1 with cash #2 with a voucer #3 with AmEx. In what order do they get picked up?
#1 first because they're afraid if they make you wait too long you'll hop and a cab (since you're paying cash) and they'll lose the fare.
#3 second because though you want to pay credit if it's too long, you might hop a cab.
#2 last because they know they're got you, since you want to use a voucher (someone else's money--generally).