In most (Swedish) homes, there are electric stoves that go from 1 to 6, and in some cases all the way up to 12!
Is there an agreed-upon standard deciding roughly what temperature a number corresponds to on the stove-scale?
Short answer: no, there's no standard scale.
First of all, I'm pretty sure it's common enough for stoves of varying power to use the same range of numbers. I see an awful lot of stoves that go up to 10 in the US, and I'm quite confident they're not all the same.
Second, the real property of a stove is its power output, not its temperature. You can clearly see this if you go look at gas stoves - they're described in units of power (BTUs in the US, hooray). The temperature resulting from a given power will depend greatly on what you're cooking. A burner with nothing on it will have a much higher temperature than one with a heavy pot of boiling water on it. To a lesser degree, the temperature will also depend on the environment - a cooler room with some air circulation will keep the burner a bit cooler than a warm room with still air.
So, if you really want to know what you're getting, you have to look up the power output of the stove - or failing that, maybe try to measure it yourself.
There is no industry standard, and stoves heat up to different temperatures. In fact, different hobs on the same stove often have different temperature when turned to the same setting (with the smaller hobs tending to be cooler).
You could try to make a crude calculation based on energy input, but this has so big an error margin that it is unusable for any practical purpose (unless you happen to know the stove's efficiency, the hob's energy consumption, mass, the specific heat of the hob material, its density, and, because it is losing heat to the air, its thermal conductivity and its surface area) But all of this applies only to the heat of the hob, not to the heat of a pan placed on it, which varies considerably with a pan's material and geometry - and when cooking, the temperature of the pan is more important, but the one that actually matters is the temperature of the core of the food pieces. So the only really good way is to measure the oil in the pan with an infrared thermometer (for frying; for cooking, use a confectioner's thermometer dipped into the food).
If you are fine-tuning meal preparation (like trying to produce a very juicy steak without leaving it medium rare), the thermometer is practically indispensable (unless you are willing to spend lots of effort on a trial-and-error procedure whose results will only be valid for a single combination of a hob, pan, and oil amount). There are ways to notice important temperatures without a thermometer, by observing typical chemical reactions and physical behaviors which occur at certain temperatures, but you need to have observed the reactions closely before, because simple descriptions of the changes are sometimes misleading. It is easy for simmering temperature ranges between 90°C and 100°C, where the amount of bubbles of water placed in a pot is easily observed. For frying temperature ranges, you can use some tricks including wooden spoons, white bread, and water drops, but they are not very precise, and you need to know what to look for. Smoke observation is easy if you know your oil's smoke point, but if you reach it, you know you have overdone it. For low temperatures (melting chocolate), a thermometer is the only way I know of.
One thing to be aware of is that increase of temperature is not always linear with setting. I have a stove with settings from 1 to 6, and at 3, the pan stays under 95°C, while at 4, it (the same pan) goes to something like 180°C or more. The other settings have different temperature differences. So be very careful when cooking.
If you are planning to buy a new oven and are looking for a comparison basis, go with their wattage, as stoves with a higher energy consumption will be hotter within a given technology (don't compare energy consumption of a resistive vs. an induction stove).
If your question is just fueled by curiosity of "how high can it go", the answer is way too high". On induction, using a cast iron pan, I managed to pass the autoignition point of oil (~375°C) and get a small fire in the pan at the 1500 Watt setting, and the unit goes to 2100 Watt (it has heat protection, but it didn't switch on until it was too late). There are many induction stoves which have single hobs maxing out at 3.6 kW, so in theory, they could get a lot hotter. And if you think "this is how modern technology works", old stoves can get very hot too, especially if they have no heat protection. My mother has an old cheap one in her kitchen, I think that the big hob is 1800 or 2000 Watt, and after half a day of charring peppers, I had the ironplate hob glowing a visible red, so it must have had over 500°C (the hob only, there was no pan on it).
To sum it up: The theoretically possible maximum temperatures are way hotter than needed (or safe) in the kitchen. The actual temperatures at each setting vary from stove to stove and need to be measured. If you are buying a new one, don't worry about the possible maximum temperature of a single hob, there are more important factors. If you have a recipe which gives a temperature and you need to figure out the setting, use a thermometer. If you have a recipe which only gives the setting for a type of stove you don't have and are trying to deduce the needed setting for your own stove, your best bet is to learn which group of proteins and carbohydrates needs which temperature for denaturing/hydrolizing/whatever, to analyze which reaction the recipe is trying to achieve, and to use a thermometer to turn your stove to the correct setting. If you don't want to delve that deep, you'll need to experiment a lot with each recipe until you get decent results.
Red hot 600 degrees Celsius Orange hot 700 Celsius Yellow hot 800 Celsius
Unusual for an element to go past 600