Lots of possibilities, which do depend on the type of valve. For the Thermarest type, which most pads use, you can even use a large garbage bag with a small hole in one of the bottom corners, held onto the valve with a rubber band. The bag of course has other uses (not for garbage, though--you don't want rotten food in your pad!). There's the Big Agnes Pump House, which works well as a pump (takes practice) but is a failure as a dry bag.

For Exped pads (the UL series that don't have the built in pump), there's a gadget called the Schnozzle. It works quite well. Some folks pack their sleeping bag in it, but I'm a bit dubious about its waterproofness.

The problem with large plastic bags (as in the video) or the garbage bag or the Schnozzle is that in your normal lightweight one or two person backpacking tent, there's not enough room to deploy it properly!