Why was 4mA and 20mA picked? Was it an arbitrary choice? I don't see this signalling method used much in hobbyist projects, why's that? What are these current signalling loops best for?
4-20mA loops are used a lot in industrial environments. The current signal is generally less susceptible to noise and signal loss over long cables. It's especially popular for things like transducers, where the transducer is actually powered with the signal line. This allows a 2 wire connection, where one line supplies the power rail (typically 24V) and the current returned is based on the measured value (temp, pressure, etc.). This can help save money on wire in a large plant, but most hobbyist probably don't care about such things or need to worry about electrically noisy environments. 4mA allows a minimum current draw by the transducer even if there is no signal. It also provides trouble shooting capability, allowing to distinguish between a signal of 0 and a lost connection or powered down unit. I don't know where 20mA came from, but 20mA is easily dropped over a 500 Ohm resistor for a 0-10V signal or over a 250 Ohm resistor for a 0-5V signal.
The 20mA current loop goes back to old school teletype, the sort of thing you might have encountered in the 1950s.
I agree with JustJeff - this just sort of happened. Since it's a signal and not power, you don't want current to be too high (so you can use low gauge wire). 20mA is not too high - comparable to what you might find in a DIO port on a microcontroller if you're lucky. It's at least a range of values that work.
I've seen them used in situations where voltage signaling just doesn't cut it. Current in one end of a wire is current out at the other. This isn't true for voltage - especially for long wires. There will be significant voltage drop over distance which can affect your readings. The current signal doesn't have this problem.