It's off topic for the language aspect of the forum, but I recently became aware of some new genealogical resources at the National Library of Ireland which could be of interest to forum users, so I'm posting info here, and adding some info about other good sources.
NLI has digitized Catholic parish registers from all over Ireland, mostly from the 19th century but some going back into the 18th century, and they've recently been made available online at this site:
http://registers.nli.ie/What they've done is to take existing microfilms and make each image (usually, two facing pages from the register) available online as an individual jpg. To judge from the ones which I've searched thus far, the records are normally very clear and relatively easy to read. Sometimes there are handwriting peculiarities to decipher, but generally not many. Just be aware that first names are frequently abbreviated by the parish priest, so you have to know things like Jas = James and Hon = Honoria (occasionally, also m first names are given their Latin form, if it exists). The hardest one I've had so far was a few cases where Jno = John.
The NLI site has copies of baptismal registers, marriage registers, and in some cases death records (in my grandmother's parish in Mayo, they had records for 40 years of births and marriages, but of deaths for just one of the famine years). The types of records and periods covered vary by parish. You search by the parish name, and there's an interactive map of the parishes of Ireland (which is fun all by itself) in case you know the right area but are not sure of the parish name (which can be different from the name of the locality or even the name of the physical church building).
For later periods, there are various more comprehensive government sources, including the 1901 and 1911 census records for Ireland which have been available online for some time at this National Archives of Ireland site:
http://www.census.nationalarchives.ie/Most earlier census records were destroyed, unfortunately, though you can find bits of them at that site, and also in other places, such as in Irish pension records.
For those who are unsure of what they have or where to search, the LDS Church microfilmed a huge number of Irish parish registers and other records years ago, and has been working to index them by name for years now. You can search on their free database, FamilySearch, at an LDS Family History Center (FHC), which are located all over the US and Canada, and in other countries (I know, because I found that relatives in Ireland had created records there). You can also create your own (free) account and search from the comfort of home. Check them out at:
https://familysearch.org/FamilySearch is what you might call "distantly related to" the commercial product Ancestry.com, but is free, as I mentioned. You can, by the way, also search Ancestry for free at the LDS FHC's, but only on site. What you can also search there for free is a European equivalent of Ancestry, called MyHeritage, which I've also found useful.
FamilySearch also has millions of other records, including census records and vital statistics records, and is expanding and adding new features all the time (sometime new features suddenly show up while you are using it). You can create, store, update, and display (in color) your own family tree there, and once you create records the system actually looks for related records and offers them for your consideration, along with various hints. Plus, you may find that someone else has already done part of your family tree, and you can link into it and update it. I've had that happen several times in the various branches of my family tree, and even located a "long-lost" branch of the family in another US city that way. Once you create a record, it also becomes available for someone else searching by name (and they protect personal info in records of living people).
I'm updating this to add some more info. There is a home software program called RootsMagic which you can buy online (for $19.95) which allows you to set up your own family genealogical records, pedigree charts, etc., and exchange info directly with the FamilySearch database which is discussed above. You can get the software at this site:
http://www.rootsmagic.comYou'll see some discussion there about RootsMagic replacing/updating an older program called PAF. It's referring to an older LDS software program, Personal Ancestral File (PAF), which can be updated to work with FamilySearch through RootsMagic, but you can ignore that whole discussion if you don't already have PAF files. The RootsMagic software which you'll get at their site is also fine for those just starting out who never had any experience with PAF or who have no PAF records to convert.