Harvest Moon - 2008 was released on:
USA: 9 May 2008 (Zompire: The Undead Film Festival)
The Harvest Moon - 1920 was released on: USA: 25 April 1920
Shine on Harvest Moon - 1932 was released on: USA: 6 May 1932
Harvest Moon - 2002 was released on: USA: 13 June 2002 (Waterfront Film Festival)
The Current release date for Harvest Moon Tree of Tranquility is July 14, 2008. But this date is subject to change.
It depends in which Harvest Moon you are playing. Most Harvest Moon games have Heart Events which aren't exactly like dates but there are a few Harvest Moon games were you do go on actual dates.
Moon Machines - 2008 was released on: USA: 16 June 2008
The Moon and He - 2008 was released on: USA: 7 April 2008 (AFI Showcase)
Swimming Moon - 2008 was released on: USA: 3 May 2008
Camp - 2013 Harvest Moon 1-8 was released on: USA: 28 August 2013
Paper Moon - 1974 Harvest 1-8 was released on: USA: 31 October 1974
Another Harvest Moon - 2010 was released on: USA: 6 October 2010 Italy: 2 November 2011
Fat Albert and the Cosby Kids - 1972 Harvest Moon was released on: USA: 31 March 1985