If you’ve worked with radios or other high-frequency circuits, you’ve probably noticed the prevalence of 50 ohm coax. Sure, you sometimes see 75 ohm coax, but overwhelmingly, RF circuits work at 50 ohms.
[Microwaves 101] has an interesting article about how this became the ubiquitous match. Apparently in the 1930s, radio transmitters were pushing towards higher power levels. You generally think that thicker wires have less loss. For coax cable carrying RF though, it’s a bit more complicated.
First, RF signals exhibit the skin effect–they don’t travel in the center of the conductor. Second, the dielectric material (that is, the insulator between the inner and outer conductors) plays a role. The impedance is also a function of the dielectric material and the diameter of the center conductor.