You can download the latest development version from github.
The latest release is 3.7.2.
For older releases, see the release history.
The following is a list of additional data files useful for Nominatim installations:
country_grid.sql.gz (mandatory from 3.0.0, included in release tar balls)
Base geometries for all countries.
Additional postcode data for Great Britain.
Additional postcode data for the United States.
Data for result ranking based on Wikipedia.