Moving Men Furniture Sliders are smooth frisbee-shaped polymer disks, either 7″ or 3 1/2″ in diameters, filled with a spongy material (they call it a special grip pad). They are an improvement on the “furniture coasters” my mother used to put under the sofa in that the special grip pad does really work, allowing you to move furniture easily. They work on carpet, though our experience has involved sliding things over berber and low-ply (we’ve never owned shag).
We have moved some pretty heavy furniture using them. You *might* be able to slide an upright piano this way — but I would leave moving a grand piano to the professionals.
These also work well for slipping under boxes on moving day.
[Although "Moving Men" are no longer available, there are several similar, effective products out there, including the ones mentioned below. -cc]