Yom Kippur, the Day of Atonement, begins on the sunset of Friday, the 29th of September and ends the following evening on Saturday, September 30th.

In the Hebrew calendar it falls on the 10th of Tishrei.

 See also:
  Yom Kippur Overview
  Fasting on Yom Kippur
  Yom Kippur Crash Course
  Aish.com's Yom Kippur e-Book