Women should expect few if any problems traveling in Ireland. Women are accepted traveling alone or in groups in virtually every environment, and gone are the days when women were expected to order half-pints of beer in pubs, while men were allowed to order the bigger, more cost-effective pints of ale. In fact, the only time you're likely to attract any attention at all is if you eat alone in a restaurant at night -- a sight that is still relatively uncommon in Ireland outside of the major cities. Even then, you'll not be hassled.
If you drink in a pub on your own, though, expect all kinds of attention, as a woman drinking alone is still considered to be on the market -- even if she's reading a book, talking on her cellphone to her fiancé, or doing a crossword puzzle. So be prepared to fend them off. Irish men almost always respond well to polite rejection, though.
In cities, as ever, take a cab home at night, and follow all the usual advice of caution you get when you travel anywhere. Essentially, don't do anything in Ireland that you wouldn't do at home.
Note: This information was accurate when it was published, but can change without notice. Please be sure to confirm all rates and details directly with the companies in question before planning your trip.