From a fun little article by Andrew Gelman and Deborah Nolan:

The law of conservation of angular momentum tells us that once the coin is in the air, it spins at a nearly constant rate (slowing down very slightly due to air resistance). At any rate of spin, it spends half the time with heads facing up and half the time with heads facing down, so when it lands, the two sides are equally likely (with minor corrections due to the nonzero thickness of the edge of the coin); see Figure 3. Jaynes (1996) explained why weighting the coin has no effect here (unless, of course, the coin is so light that it floats like a feather): a lopsided coin spins around an axis that passes through its center of gravity, and although the axis does not go through the geometrical center of the coin, there is no difference in the way the biased and symmetric coins spin about their axes.

On the other hand, a weighted coin spun on a table will show a bias for the weighted side.  The article describes some experiments and statistical tests to use in the classroom.  There are some entertaining stories too.  Like how the King of Norway avoided losing the entire Island of Hising to the King of Sweden by rolling a 13 with a pair of dice (“One die landed six, and the other split in half landing with both a six and a one showing.”)

Visor volley:  Toomas Hinnosaar.