You can currently snag tickets from New York to Tel Aviv Israel nonstop for $812 round trip. This nonstop fare is available with Elal, and Delta Airlines, for departures on select dates during March, (not all dates are available, you have to be flexible and search different dates within March). There are more dates available for flights on Elal. Also, with Elal, Besides for returning during March, there are also fares available with returns on April 16th 17th 18th and the 30th for the same price.
Alternatively, You can snag tickets with a stopover from $696. During January there are flights available with Transaero Airlines (they allow 2 free bags) for $696 round trip. During February there are tickets available for $726.
With Orbitz, you can cancel your ticket free of charge till 10pm CST the day after your booking. With priceline, you can cancel your ticket free of charge through 11:30 pm EST the day after you purchase your ticket.