AutoCAD 2016 now offers a Geometric Center object snap. This was the #2 item on the AUGI wishlist.
When using the Geometric Center osnap you can snap to the geometric center of Closed Polylines, including Polygons and Rectangles. The Geometric center osnap appearance on screen is similar to an 8 pointed asterisk.
You can access it through the command line by typing GCE and works similar to all of the other AutoCAD object snaps. It can be set running (or ran as an override) using the same traditional AutoCAD osnap access and setting methods; including the Drafting Setting dialog box, the Status bar, and the Right+Click contextual menus, (including the Shift+Right+Click menu).