No, not for normal interpretations of "radio". Think about it. If there were such a frequency range, lots of people would be abusing it, thereby making it unusable. That's why we have a central authority that allocates space. Doing so is in everyone's interest, even if not in individual interests.
It's a lot like the rules we have for driving on a specific side of the road. If there is a traffic jam one way and little traffic the other, you as one person would be better off driving on the other side of the road. However, when everyone does this, as they would if there weren't any rules, we'd have a dangerous mess, and everyone would be worse off.
You can use much shorter wavelength, like IR and visible light, pretty much any way you want for communication. Even then, you can't go lighting your neighbor's house on fire with a stron IR beam or point a laser in the eyes of airplane pilots.