Census Records
It's when you get to census returns that you'll run smack dab into wholesale destruction of archived records; in this case, destruction involved both fire and governmental shortsightedness.
In every district in Ireland, the government conducted censuses every 10 years, from 1821 to 1911. The 1922 fire at the Public Record Office in Dublin almost completely destroyed the census records for 1821, 1831, 1841, and 1851, except for a few surviving fragments; the census records for 1861, 1871, 1881 and 1891 were entirely destroyed by governmental edict. However, the comprehensive census returns for 1901 and 1911 have survived, and you can research them on microfilm in the National Archives of Ireland. If you are interested in the 1901 census, you can view a complete microfilm copy at the LDS Family History Library in Salt Lake City and through local Mormon Family History Centers. In addition, you can track down 1901 Northern Ireland census records through the Public Record Office of Northern Ireland.