It has been estimated that over 533,000 indentured servants came to colonial America between 1630 and the beginning of the American Revolution in the 1770s. They were mostly young people who agreed to work for a set number of years in exchange for a voyage to America and the provision of food, shelter, and clothing for the duration of their debt bondage.
Since they came before 1820, there is no official set of passenger lists that can be consulted for more information about their arrival. Therefore, other documents must be consulted to establish primary and secondary evidence of their existence.
Since 2007, the Immigrants Servants Database has added information about such indentured servants. Currently, the database contains over 20,000 names for the time period 1607 to 1820. A small percentage of these, roughly 510 in total, are verified as coming from Ireland.
For example, Patrick Malone, birth nation Ireland, was born or christened about 1753, and was indentured near Baltimore, Maryland. There is an interesting observation in his entry that he "speaks quick, and a good deal on the brogue." Even earlier, there was Edmund Ryan, born or christened about 1719, whose occupation was a nailer.He was indentured in Milton, Massachussetts and his master was Thomas Craddock. Some entries are even more detailed concerning the persons place of origin. Katherine Arch-Deacon, originally from Bramhall, Co. Kilkenny, was indentured in 1704.
Like all good historical/genealogical research, there is a citation to lead you back to where the information for each entry was gathered from.
Treatment of these indentured servants varied widely and for various reasons they absconded. This lead to their masters placing reward advertisements in newspapers of the era, such as this collection of adverts in 18th century Virginia newspapers, some of which are for absconded Irish people.
 Kulikoff, Allan. 1986. Migration and Cultural Diffusion in Early America, 1600-1860 in Historical Methods. Vol. 19. pp. 154-155.
 Immigrant Servants Database, database; http://www.pricegen.com/immigrantservants/servant/show.php?servant=15090: accessed 9 August 2013; entry for Patrick Malone; citing Tom Costa, Virginia Runaways, The Geography of Slavery in Virginia, accessed 13 March 2007, quoting Virginia Gazette [online image].
 Immigrant Servants Database, database; http://www.pricegen.com/immigrantservants/servant/show.php?servant=19847: accessed 9 August 2013; entry for Edmund Ryan; citing Michael P. Quinlin, Irish Boston: A Lively Look at Boston's Colorful Irish Past, pages 1-2, quoting New England Weekly Journal.
 Immigrant Servants Database, database; http://www.pricegen.com/immigrantservants/servant/show.php?servant=5031: accessed 9 August 2013; entry for Katherine Arch-Deacon; citing Elizabeth French, List of Emigrants to America from Liverpool, The New England Historical and Genealogical Register, Vols. 64-65 (1910-1911), quoting Liverpool Town Books 1697-1707, Liverpool Record Office, Liverpool, England.