I've been told that the shiny side should go on the inside for cooking, and the outside for freezing. In other words, do you want to reflect the heat into the food, or away from the food?
However, common sense (which fails very often) tells me that with the temperature ranges involved, any benefit is marginal, if it exists at all.
The only time it might matter, is if you were trying to warm something up in the sun. Then it might make a difference.
EDIT: From The Straight Dope:
The truth is that the shiny side is
not treated with a dangerous chemical.
Mineral oil is used as a lubricant
during the rolling process, some trace
of which may remain on the finished
foil--but it's not dangerous. The
shiny side is shiny because of the way
foil is made. During the last pass
through the rolling mill, a double
thickness of foil is run between the
rollers. The side of each sheet that
comes in contact with the polished
steel rollers comes out shiny. The
other side has a matte finish.
The official word from the Reynolds
aluminum people is as follows: "It
makes little difference which side of
the Reynolds Wrap aluminum foil you
use--both sides do the same fine job
of cooking, freezing, and storing
food. There is a slight difference in
the reflectivity of the two sides, but
it is so slight that laboratory
instruments are required to measure