The National Archives of Ireland Genealogy Page is a good starting point to see what's there.
The on-line database for the Ireland to Australia convict transportation index 1791-1868 is here. This wonderful gift by the Irish government to Australia for our bicentenary is on-line, thanks to the generosity of the Irish government. However users should note that the database is incomplete in that certain types of records are not present. Many Irish convicts transported to Australia will not be mentioned in the database. If you want more information on what's in and what's not click here first
Lesley Uebel's Claim a Convict site, which has lots of convict and other information and links to other interesting sites
The LDS's Family Search Home Page, a wonderful resource.
George Bell's Original Indexes for the North-East of England are a unique resource. It was through George's indexes that I made a breakthrough after a decade and obtained an 1816 newspaper account of the trial of one of my convict ancestors. The convict story is told in Sixpence. Sadly, George has passed away, but his work is available at Ancestral Indexes eShop
State Library of Victoria, which has a wonderful online multimedia catalogue.
National Archives of Australia
The Australasian Legal Information Institute has a comprehensive legal database that can be useful.