Craig, one of our regular dancers, drove over to Seattle recently to attend a dance workshop there and discovered upon arrival that he had forgotten to bring his dance shoes. So he ran to the nearest drugstore and bought some moleskin, which has a surface similar to the suede used on professional dance shoes. He stuck the moleskin on the bottom of his running shoes and reports that it worked so well that he had to cut a few pieces out to make them less slick. Duct tape is reported to work well too. In fact, you can use either of these to convert an existing pair of shoes that you love into dancing shoes.

Running shoes with moleskin on the bottom (some holes cut out to reduce slickness)
Running shoes with moleskin on the bottom (some holes cut out to reduce slickness)