So... why are they green? Since I didn't know, I turned to Google. My favorite answer was, well, for the same reason jeans are blue and New York taxis are yellow. Which, actually, isn't strictly true.

Many different theories…
There seem to be numerous theories about why a PCB is typically green: from the US Army deciding it would be their standard color, which then became the norm, to the contrast during assembly being pleasing to the eye, or the fact that green is environmentally friendly (a deciding factor 100 years ago?).
The first PCBs date back to the early 1900s, but they really gained recognition when they began to be used in early designs of vacuum tube radios and gramophones in the 1920s. In the 1950s and 60s, defense agencies used laminates of different blended resins for new weapons and communications systems.

A mixture of different colors.
It was at that time that the solder masks used contained a base resin, which was a brownish-yellow, and a hardener that was a deeper, muddy brown. When mixed, they created a honey-brown color, which wasn't particularly attractive. They tried adding red pigments, which then turned into a rusty color, and later, using a blue pigment, they only managed to achieve this darker brown. None of these experiments produced very attractive colors since the base laminate at that time had a green tint. So, they tried adding yellow and blue pigments to obtain an acceptable green, which later became the standard we see today.
This seems to be the most logical reason why PCBs are green, and perhaps it also seems a somewhat simple or boring reason.