But there is a medium for waves-- in the case of electromagnetic waves, the medium is the photon; in the case of "matter waves" (which actually do exist, although it's more of a "statistical" wave than something that's really moving as a wave) it's the components
of the atom. Quantum mechanics says that everything (both matter and energy) has the property of wave-particle duality, where in some situations it behaves as a particle, while in others, it behaves as a wave-- it's trivial to show both the wave and particle
nature of light in any high school physics lab, while the wave-particle dualtiy of matter is more difficult to show and requires some pretty specialized equipment.
There is not, however, any kind of common, omnipresent medium in which energy and matter waves travel (according to our current understanding of physics)-- that's the concept of the lumniferous aether, which has been thoroughly debunked for about a
century (specifically, relativity doesn't work if you have the aether, and the laws of relativity can be shown to be an accurate description of reality fairly easily-- the doppler effect in light is one example (in that you can measure the relative velocity
between the two objects and calculate the doppler shift of the light without having to know the relative velocity of the medium in which the waves are traveling-- this becomes important when measuring the doppler shifts of objects in space).
If you'd like some more information (in a pretty readable form), I'd recommend
Six Easy Pieces (for quantum mechanics) and
Six Not-So-Easy Pieces (for relativity) by Richard Feynman. I haven't read them myself (yet), but I've heard wonderful things about them, and Feynman is most definitely one of the most talented writers amongst the modern physics community. They're available
from Amazon or should be available from your local library.