What is the shortest day in 2009?

Northern Hemisphere - December 21
Southern Hemisphere - June 21
These dates are often referred to as the Winter Solstice.

Historically, Christmas Day was set by the Roman Emperor Constantine. When he converted from Paganism to Christianity, he identified Jesus with the Pagan Sun God. The Winter Solstice is when the days start to get longer, and may thus be regarded as the birth of the Sun.