I know of a few ways to thicken sauces and the like:
- Egg (protein)
- Flour (protein / starch)
- Starch (cornstarch etc)
- Reduction (reducing watery component)
Are these the only common ones, or what else should a cook keep in his repetoire?
Major ways of thickening a sauce -- or, for that matter, some other liquid:
Note that some of the examples of one category can also fit into another.
What you listed are definitely the most common ways to thicken a sauce and most chefs stick to these basics.
However there ways I can think of to thicken sauce that you haven't mentioned.