Ellis Island: http://www.ellisisland.org/search/pass
US National Archives/Immigration info: http://www.archives.gov/research/immigration/
The Boston Pilot; From October 1831 through October 1921, the Boston Pilot newspaper printed a Missing Friends column with advertisements from people looking for "lost" friends and relatives who had emigrated from Ireland to the United States. This extraordinary collection of 40,743 records is available here as a searchable online database, which contains a text record for each ad that appeared in the Pilot. http://infowanted.bc.edu/
The Irish in Argentina - The Immigration Museum in Buenos Aires run by the Department of the Interior has individual cards with the names of Irish immigrants stored in their archive. The Museo Nacional de la Inmigracian (open 10 a.m. - 5 p.m. weekdays, 11 a.m.6 p.m. weekends. tel. 011/43170285, firstname.lastname@example.org) is free
AUSTRALIA: Generally, more information was given at the port of arrival rather than the port of departure. The University of Woolongong has produced, on microfiche, a complete index and transcript of all information concerning immigrants of Irish origin recorded on ships' passenger lists between 1848 and 1867. These are useful for finding out an exact place of origin as well as parents' names. The Public Record Office of Victoria has good online databases of settlers at www.prov.vic.gov.au
Otherwise, other records may be found in the Colonial Office Papers of the UK National Archives, class reference CO 201. This class contains a wide variety of records, including petitions for assisted passages, emigrants' lists, records of emigrants on board ship, petitions from settlers for financial assistance and much more.
NEW ZEALAND: There are lots of books and documents available about the Irish emigration to NZ. There is a website you could look at: http://www.teara.govt.nz/en/irish/2 for information about the Irish in New Zealand.