Because the rooms in your home have cold-air returns as well as heating vents, shutting the vents doesn't prevent air movement. Just like closing doors to prevent air flow, it interferes with your home's energy efficiency. It creates pressure in the closed-off room, which causes the return duct to pull in cold air from any cracks in windows or doors. In addition, the warm air still trying to push up through closed vents will start to leak out any ducts that aren't sealed properly, or it will be forced back down into your basement or into floor cavities. So, you'll still be paying energy costs for heat, just in places you can't use.
It's also possible to damage your furnace by closing too many air vents. Newer, high efficiency models are designed to operate with your specific square footage in mind and with fans running at full speed. Closing off vents creates unexpected blockages, which forces the furnace to work harder when distributing heated air. It's also possible that limited air flow, especially in winter, may cause freezing in your ducts, meaning more work for your heating and air conditioning system. So this not only lowers the energy efficiency of your heater, but shortens its life.