The number of faces (polygons) is displayed in the Info Header at the top.
The default cube:
After adding a Subsurf Modifier it has 96 faces (2 subdivisions:
In a complex scene with multiple objects you would need switch to Edit Mode or move the object to an unused layer M to see only the number of faces for a particular object.
Before applying the modifier it is also a good idea to change toWireframe display mode to get an impression of how dense the mesh actually is.
The subdivision divides a face into four faces (per level) as mesh subdivision would do. Here an example with algorithm Simple because it appears more obviously.
Catmull-Clark:
The rough rule derived from the above info (without studying the paper) is
sub_faces = origianl_facesoriginal_faces * 4 * subdivision_level
it doesn't cover triangles and n-gons. For a more detailed describtion see:
Subsurf (thanks to @cegaton)
It provides formulas based on the number of vetices which seem to be more accurate.