This thread has me worried. I am moving back to New York after a semester abroad and have to bring 2 checked bags on 2 flights on 2 airlines with a 2 day stopover in Dublin.
Don't worry about this if your traveling any of the mainline (Lufthansa, AirFrance, TAP, LOT, Alitalia, BA, Aer Lingus, etc) European airlines into Dublin. If your on one of the low cost carriers (EasyJet or similar) than you will have to pay for the checked luggage. For the Dublin to US flight its an international flight so you can check pretty large and pretty heavy bags (50kg or less per bag I think). There most likely won't be any extra fee for this unless you are flying one of the US carriers home. The US carriers will charge you something like 25$ for the first bag and 75$ for the second bag, unless you are booked into premium economy or have airline status.
Either way the process inside the EU and from the EU to the US is usually really good.