Is it possible to move parts of a model along the selected normals? For instance, if you have a object that lies flat on the ground plane, then you can select the edges, push G then Z and move those selected edges straight down, in this case it would be as if the selected components were moving along the normals like how the extrude tool behaves. 

However, if the object is rotated about several axis then this method will not work, so my question is this. Is there a way to move selected elements along the normals in the same way that extruded elements move away from an object?

Any help on the matter would be greatly appreciated.
You can set the Transform orientation to Normal in 3D view > Header:



This will align the Z to the normal of the selected element. (Or in the case of multiple selected elements, the average of the normals of all selected elements):



Note that pressing GZ will still move the selection along the global coordinates, to move the selection along the orientation set with Transform Orientation you need to press the axis key twice (so GZZ).