A lot of web pages claim that sugar caramelizes at ~160C. But also a lot of recipes caramelize sugar in a simmering water. The boiling point of water is only 100C. So how can these recipes succeed so well in practice?
a lot of recipes caramelize sugar in a simmering water.
Calling the solution "simmering water" isn't a good characterization. The boiling point of pure water is 100C. But the boiling point rises as the concentration of sugar in the solution increases. Once you're above 75% or so, the boiling point increases significantly. For 90% sugar (still 10% water remaining), it's up to around 120C.
As the water evaporates, the sugar concentration, the boiling point, and therefore the temperature all increase. When you reach 160C, there's probably less than 1% water and the decomposition of the sugar (carmelization) rate starts to increase significantly.
There are some charts/tables for different concentrations here, but they only goes up to 90%
Recipes that call for water to be added to the sugar for making a caramel do so to help all the sugar melt, by dissolving some or all of it in the water. This prevents premature crystallization of the sugar. When you keep heating the mixture, all the water will evaporate, at which point the temperature of the (now pure) molten sugar will rise above 100 °C and will go through its different cooking stages. The sugar will caramelize when it reaches a temperature of 160 °C.
While the other answers are right, it should be pointed out that caramelisation does not happen at 160°C - not only at that temperature, at least. Thermal decomposition happens as both a factor of temperature and time. In fact, it is possible for sugar to undergo thermal decomposition well under 160°C: Stella Parks over at Serious Eats does it at 150°C, and Harold McGee has done it at 125°C