Irish passport holders may enter the USA under the Visa Waiver Program as long as they meet the relevant requirements. See here:
http://travel.state.gov/visa/temp/without/with out_1990.html
The key elements of those requirements are that you should be travelling solely for the purposes of tourism or business and that you should not have a criminal record. There are certain exceptions to the 'convictions' rule. If you need to view them, see here:
http://www.travel.state.gov/visa/frvi/ineligib ilities/ineligibilities_1364.html
Chris