Press SHIFT-DKEY to create an identical copy of the selected objects. The copy is created at the same position, but is automatically in Grab mode.
This is a new object in all senses, except that it shares any Material, Texture and IPO with the original. This means that these attributes are linked to both copies and changing the material of one object also changes the material of the other.
You can make separate materials for each, as described in the Materials Chapter if you need.
You can, on the other hand, make a Linked Duplicate rather than a real duplicate by pressing ALT-D.
This will create a new Object having all of its data linked to the original object.This implies that if you modify one of the linked Objects in EditMode, all linked copies will be modified too.