Snap to grid in edit mode For some odd reason, each vertex thinks of it's own grid. 


I want to snap them along the grid line above them, but the result is this:


What's wrong?
Activate the Absolute Grid Alignment option



EDIT In your case it seems to not working because of the armature, Blender can't figure out how to snap the vertex the final transformation of the vertex to the grid because of the deformation introduced by the rig.