What causes curdling and how can you prevent it?
In most cases, curdling occurs because proteins in the sauce are denatured and bind up with each other forming clumps.

In cooking, proteins are denatured by excessive heat, acid, salt, or enzymes.

Heat and acid are the usual culprits for me. For example, when making a hollandaise sauce- the egg yolks are slowly cooked to allow them to set. In most recipes the lemon juice is added later. If the sauce is heated too abruptly or too high then the egg proteins will curdle.

To prevent curdling you have a few options-  


Don't expose the sauce to as much heat.
Be careful to not overcook egg rich sauces. If possible add the protein rich ingredient later in the process- for example adding yogurt to a sauce just before serving.  
Heat the sauce gently.
Heating too fast will also make proteins denature. Many sauces are cooked in a double boiler- not to keep the sauce from overheating but to ensure that it heats gently.  
Don't expose the proteins to too much salt or acid.
Dropping a couple tablespoons of lemon juice into warm milk is a recipe for paneer not sauce.  
Take out some insurance.
Proteins bind with each other after denaturing when there are a large quantity of similar molecules all together. One solution then is to introduce a lot of dissimilar molecules that will interfere with the protein's ability to bind to itself. Common candidates for this are starch or fat.


It is difficult (but not impossible) to curdle the milk protein in cream based sauces with just heat because the high concentration of milk fat gets in the way. This is why reduction sauces can add cream to a very hot liquid and let it reduce. However, adding acid and heat can still be enough to curdle so be careful if your reduction sauce is very acidic.

Many otherwise fragile sauce recipes will call for a little bit of corn starch as an insurance policy. In the related question that you posted- yogurt sauces are particularly susceptible to this because low-fat yogurt is very high in protein and low in fat, and starch.