The National Archives of Ireland has released the 1901 Irish census in a free online database. All 32 counties—encompassing both of what’s now the Republic of Ireland and Northern Ireland—are covered in this census.
You can search by name, county, and other factors. You can use an asterisk as a wildcard in a surname. The site automatically adds a range of plus or minus five years to ages. (The site was slow when I tried it this morning, so you might need to let the initial rush subside before trying your search.)
The 1911 census also is searchable on the site. The 1901 and 1911 censuses are the only surviving full Irish censuses open to the public.
The Irish census is unique because you can see the original household manuscript returns (the forms filled out by the head of each household on census night), rather than just transcribed enumerators’ books.
The basic topographical divisions for the census are county, district electoral division (or DED), and townland or street.
A number of townlands/streets are missing from the database 1901 and 1911. According to the Irish national archives website, these forms weren’t microfilmed or digitized. The material will be put online as soon as possible.
More Irish genealogy resources from Family Tree Magazine.