Most parts of Ireland speak English. Every one we met certainly did. Our chauffeur, David, told us that there was a whole portion of the country in which the traditional Irish language, Gaelic, was spoken. The Irish government is extremely protective of Irish culture ever since they "separated" from Great Britain. They even go so far as to require students to spend a few weeks in this Gaelic-only region in order to make sure the language is preserved throughout generations.
Indeed, every road sign we saw while traveling, from the inner parts of Dublin to the fringes of the Dingle Peninsula, there were Gaelic words underneath the English. Go Mall. Became a common phrase: slow down. The roads in Ireland are so small and so close to falling off of the average cliff that it was possibly the single most repeated phrase we heard or saw on the trip. The Irish accent (in English) is also very interesting. In addition to more normal pronunciation differences, the Irish always pronounce "th" like "t", so you would often hear phrases like "It's tree tirty four." After a while I became so used to this specific pronunciation that I was confused when a grocery clerk was saying "turkey", and I wondered to myself what a "thurkey" was.