Yom Kippur, the Day of Atonement, begins on the sunset of Tuesday, the 18th of September and ends the following evening on Wednesday, September 19th.

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