Cheap Flights to Ireland and Israel: From $379 Total Roundtrip!
Per this Flyertalk thread there are cheap fares on many airlines from New York and Boston to Ireland.
Star Alliance: United/Lufthansa/Air Canada have many routings- both nonstop and connecting via Frankfurt and Toronto/Montreal.
There are many ways to search for these fares, the easiest probably being Travelocity's Flexible Date tool.
Travelocity.com -> NYC - DUB -> Flexible Dates -> Now through March
You'll see results for Air Canada (but they have higher taxes and route via Canada and London so they end up being more expensive), Continental, Lufthansa and Delta.
You can also book through Delta.com, which will let you cancel any itinerary up until the night of the following day.
Delta.com -> Planning Tools -> Book a Flight
Then select "Flexible dates" and you can do +/- 3 days or weekend travel by month. For mileage runners, the best MQM for your buck will be if you can route JFK-ATL-DUB. For only $50 more, you get over 3,000 more elite miles.
Last year I did my December mileage run to Dublin (from Pittsburgh, where they were running double MQMs). Maybe I'm biased since I am Irish, but I love Dublin- even in dreary winter. In early December, we had nice crisp weather and the city was decked out in holiday decorations. I find the Irish to be extremely friendly and we had a great overall 1 night trip.
Per Dan's Deals, you can get flights from NYC to Tel Aviv via Brussels for as low as $564 total roundtrip, which is unbelievable for Israel flights. I plugged sample dates 3/6/12-3/13/12 into Travelocity and got Brussels Air E fare tickets (which only earn 50% miles on United and US Airways). You can apparently get the Newark-Tel Aviv United non-stops for $815 total- and they earn full mileage.