Well, let's look at a wave in water. It moves some water around, but in a cyclical pattern that should result in very little actual work being done. The same way that lifting something gives you all the energy back when you drop it.

Maybe you're thinking of this from the perspective of a solid object moving through a medium, where it must spend energy on displacing the medium in order to move? This is where my note regarding the wave being energy is important. It does not have to displace anything to move through the medium, the same way that the heat from your stove doesn't displace your pan in order to heat your food. The energy simply goes through.