The BMD Index on FamilySearch covers civil records - so births, death & marriages from 1864, plus non-Catholic marriages from 1845.
Earlier records will be parish records not all of which survive for early dates, and it's also important to remember that not all of those that do survive are available online. The two main clues you require to check for parish records are the denomination and the location - i.e. town, townland or parish.
Shane