The National Archives has made the 1901 Census and the 1911 Census available online. The National Archive also holds the Tithe Applotment Books for the 1820 and 1830s, Griffith’s Valuation for the 1840s-1860s.
The General Register Office holds civil birth, marriage and death records from 1864-1921. www.familysearch.org contains free indexes to these up to 1958 and you have to write to, and pay, the GRO for a copy of the certificate you require.
The National Library of Ireland holds estate records, Catholic parish records and land records.
Do you think your family came from Ulster? Then search The Public Records Office of Northern Ireland.
Presbyterian records can be traced via the Presbyterian Historical Society
The Registry of Deeds has details of registered property transactions from 1708 to the present.