The holiday of Shemini Atzeret/Simchat Torah, falls on the Hebrew calendar dates of 22-23 Tishrei—Shemini Atzeret on the former date, Simchat Torah on the latter. Here are the coinciding secular dates for the upcoming years:
2010: September 30-October 1
2011: October 20-21
2012: October 8-9
2013: September 26-27
2014: October 16-17
2015: October 5-6
The Jewish calendar date begins at sundown of the night beforehand. Thus all holiday observances begin the night before the dates listed. Jewish calendar dates conclude at nightfall.
See also:
When is Rosh Hashanah in 2010, 2011, 2012, 2013, 2014 and 2015?
When is Yom Kippur in 2010, 2011, 2012, 2013, 2014 and 2015?
When is Sukkot in 2010, 2011, 2012, 2013, 2014 and 2015?
When is Chanukah in 2009, 2010, 2011, 2012, 2013, 2014 and 2015?
When is Purim in 2010, 2011, 2012, 2013, 2014 and 2015?
When is Passover in 2010, 2011, 2012, 2013, 2014 and 2015?
When is Shavuot in 2010, 2011, 2012, 2013, 2014 and 2015?
When is the Ninth of Av in 2010, 2011, 2012, 2013, 2014 and 2015?