Puncture/Tear at base of air valve.
As Kibbee suggests, the wrong size valve.
A badly-formed valve hole in the rim.  It's not that unusual to find that there is a "lip" of metal at the hole that will cut into the tube.  This requires a bit of filing with a small round file to correct.
Running the tire flat or with very low pressure.  As an under-inflated tire rolls on the ground it tends to "walk" along the rim, tugging on the valve stem.
Poor tube installation technique.  Most importantly, inflate the tube slightly before installing -- just enough that it rounds out (though it should still be limp).