The only 'free radio frequency' that I could think of are the HAM radio bands. But they really aren't free, for they are regulated by laws that require you to hold a license, restrict what purpose you can use them for, and are governed by some organization or body.
Are there any useable radio frequencies that are 'undefined'? i.e. I could use them any way for any reason without breaking any laws or be unethical.
There's the ISM bands that you can use for whatever you want, as long as you stay withing certain restrictions, mainly power level.
The 2.4Ghz band is one such ISM band, which is why there is so much traffic on it (WiFi, Bluetooth, Analog video cameras, ZigBee). For that band, I believe that the power limit is 1 milliwatt for continuous transmission, and 10 milliwatt for low duty-cycle transmission. No license or certification is required, but the FCC would come after you if you exceed the limits.
Wikipedia has a list of ISM frequencies: https://en.wikipedia.org/wiki/ISM_band
The two bands listed as "Amateur" are usable, but you need to know what you are doing.
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.
Sorry, no, at least not in the US. The FCC has allocated everything between 9 kHz and 275 GHz.
Wow, This is an ancient post but these answers are terrible and need fixed.
Look up Lowfer, Medfer and Hifer, that is 160-190kHz, the AM broadcast band and ~13.56 MHz respectively. These are available in the US under Part15 rules and probably many other countries under similar rules (look up your local laws).
Legal power and antenna limits for unlicensed use are very restrictive so you aren't going to set up a radio station or have a voice conversation across the planet.
Using low bandwidth methods like QRSS (really slow morse code) or Slow Hell (sort of draws pictures... very slowly) you can "make your presence known" across some pretty large distances. You might even cross an ocean on a very good day.
