It depends where you are from of course, but making the assumption that you are in the UK then I would highly recommend it. It used to be that you required photo ID, particularly if taking a flight to Ireland, but with heightened security measures since 9/11 then I believe a passport is very much recommended if not required, If you are flying then your airline will be able to advise you of ID required.
Again supposing you are from the UK the answer is a NO. I am very aware of this living and working in N. Ireland but as the others have said if flying you will need photographic ID though a driving licence will suffice for this.
I went from Pembroke to Rosslare harbour and back by ferry and was told that I didn't need a passport, and that my driving licence would do. Nobody asked to see it, though.