Recently I investigated a bug report and a similar thread on BlenderArtists about how to have greater control over how objects behave when parented to curves.
For instance, sometimes you want to parent one object to the curve object, so that the two components will be translated/rotated/scaled together. That is, when you go into edit mode on the curve and try to move the endpoints of the curve, the position of the child objects should not change, moving relative to the moved points.
To have child objects ignore changes to the curve path, simply disable the checkbox in the "Path Animation" panel header. This setting controls whether a "Path" (i.e. a tessellated representation of the first curve island within a curve datablock, with positions on this accessed using a parametric parameter - similar to the "Offset Factor" in the Follow Path constraint) is generated and used to determine the parent location that child objects see. It is enabled by default to make curve following animations easier to achieve.