Presenting a classic: andreas08!
Tracing Irish Ancestors is slightly more difficult than tracing those in England, Wales and Scotland as many records were lost to fire in 1922. Many do remain though and one of the best resources for Irish family tree studies is on the Origins Network site
Access
unique Irish and British genealogical data at the Origins Network
The completeness of records varies throughout country with parts of Dublin being particularly patchy.
The Irish Times has some information on tracing Irish ancestry.