Partner Ballroom Dance Robot
Well, my Britannica arrived, but they sent me the 2005 version instead of the 2006 version. Sigh. But they correctly sent the 2006 Almanac (I buy an almanac every five or ten years, even though most of the info in it is available online these days), and on a quick riffle through it I came across an arresting photo of a pair of Partner Ballroom Dance Robots, or PBDRs. (That site includes a video clip demonstration.)
A CNN article from June 2005 has more info and another photo; Engadget also has more info and another photo (and predictably dumb comments from the peanut gallery).
And then there's Kosuge-Wang Laboratory's Mobile Smart Dance Robot (MS DanceR), which they only show from behind and looks much creepier-looking to me.