Mode:Edit Mode
Panel:Tool Shelf ‣ Tools ‣ Mesh Tools ‣ Add: Duplicate
Menu:Mesh ‣ Add Duplicate

This tool simply duplicates the selected elements, without creating any connections with the rest of the mesh (unlike extrude, for example), and places the duplicate at the location of the original. Once the duplication is done, only the new duplicated elements are selected, and you are automatically placed in grab/move mode, so you can translate your copy elsewhere…

In the Tool Shelf are settings for Vector offset, Proportional Editing, Duplication Mode, and Axis Constraints.

Note that duplicated elements belong to the same vertex groups as the «original» ones. The same goes for the material indices, the edge’s Sharp and Seam flags, and probably for the other vertex/edge/face properties…