Is the world of electricity as messy as it looks?
No, not quite. Look at the statistics page. From this, you can see that in reality only 110-127V and 220-240V nominal is used for single phase and there are only two frequencies, 50Hz and 60Hz.
How much does the voltage vary?
The input voltage varies in a wide range in many countries. In North America, Great Britain and NZ/AU the voltage tolerances have traditionally been very tight, +/-5% or +/-6%. This requires costly substations and oversizing of conductors in the LV distribution. Other countries have found other places to spend the money.
In addition to this there is a voltage drop from the service cable to the socket outlet. The wiring regulations typically specify a maximum voltage drop in the 3-5% range. The worst case is thus a voltage at the outlet that is 5% of the nominal voltage lower than the minimum voltage. Luckily, this is a rather unlikely scenario. You are welcome to disagree with me. I haven't travelled the world with a voltage recorded.
What about frequency?Frequency is much more stable than voltage, as it is not affected by the distribution. It is only determined by the speed of the generator. In order to synchronize different power plants in a grid, the frequency is kept within a very tight interval. (+/-1% or better.) In addition, the grid operator often try to keep the number of cycles per 24 hour period constant, to allow the power to be used as a reference for digital clocks. With a local power plant, the frequency is not as important, and outside the developed world the frequency can fall very low. I've seen references for Romania (50Hz), India (50Hz) and North Korea (60Hz) that the frequency had been recorded at 41HZ, 45HZ and 42.5Hz respectively. Those should be extreme cases, though. Input from readers on this matter is most welcome.