How can you get a throw rug to stop sliding on a ...

An easy (and non-permanent) way to do this is to sew several rubber jar rings of the type used in home canning to the back side of the rug.

The rings are easily removed and you can still put the rug through the washer (avoid the dryer) without damage.

You can find the rings in any store that sells home canning jars and lids (sometimes even WalMart carries them) and you don't need to do more than tack each ring onto the rug in several spots - 3 or 4 per ring should do.

ccraig,

      A far easier way than sewing anything on to the rug is to simply purchase a rug mat.  there are very inexpenisive ones, made out of the same latex found on the back of most bath/kitchen rugs. You can generally find them at Bed, Bath & Beyond, JC Penny's, etc. Just purchase one a little bigger than the dimensions of your rug, and with basic household scissors, cut it to fit!!!  If you have no luck at the aforementioned stores, google search "non-slip rug pad" or "non-slip rug mat". 

Those can work, but I specifically chose not to suggest them because I have tried them and found them bothersome. It is too easy to find yourself with a corner of the rug flipped back to expose the rug mat underneath, especially if you have children and pets in the house.

A one-piece solution works better for me; which means that I would have purchased a rug with a non-skid backing in the first place - but since ccraig asked how to transform an existing rug, I gave a suggestion that should work. It requires very little cash outlay and minimal effort - if you can sew on a button, you can sew a jar ring to the back of a rug.

rubber shelf liners used for cabinets I believe will work. Pick them up at wall mart pretty cheap.