How can I copy/paste the *formatting* of a table in Powerpoint?

As far as I know, what you are asking for is not possible.

If all your tables are to have the same style, you could create a presentation template that has this one style as default table style.

Another option is to copy the table out of PowerPoint into some other Office application such as Word or Excel that is more flexible, then copy it back.

The simplest way is to just copy the whole slide and then delete the text that you don't want. That way you have an identically formatted table to work off of.

This is possible in PowerPoint 2010, a good tutorial is found Here. The power point ninja explains how to save the source formatting and not lose your colors and and cell formatting.

Not really in the manner you have asked.

If you have a corporate style that you need to use for all templates, what you would really like if for that style to appear on the ribbon in Table Tools -> Design -> Table Styles so you can just click and apply your formatting. The only way to make this easy is for someone to delve into XML and VB to make it happen. See this post for more information and an example.

The approach I follow every time I need to deal with this issue (unfortunately in PowerPoint 2010 the Format Painter do not copy the background or borders) is the following:

I copy the entire table from PowerPoint to Excel in order I can adjust the styles, change the border properties, the background, and make all the changes I need to do to the table.

When I am done, then I copy the table back to PowerPoint. Make sure you paste it in the right way (see paste special options). If you don't need to change the number of cells then the best way to paste it is highlighting the existing cells (select all the table cells) and then paste the content from Excel inside your PowerPoint table.