The next answer is a simple pan sauce.
After sauteing a protein in a pan, there are caramelized bits of fat, spice, and flesh that make for a great sauce base.
Getting those bits into a sauce takes a little work, but it's easily accomplished by adding an acidic liquid to the pan and allowing it to deglaze , or breakdown the fatty bits into the sauce.
You can deglaze with red or white wine, stock and lemon juice, or alcohol (be careful if it's high proof, since it will flame).
After adding the acid, stir to break up the bits and let simmer for long enough to reduce the liquid about 30 to 50 %, longer for thicker sauces.
Then add fat, either butter, oil, or cream, and whatever seasonings (tomato paste, mustard, Worcestershire sauce, etc.
you want in the sauce).
Simmer for just long enough to incorporate the ingredient (1-2 minutes max).
This is a good technique because it can work with any pan-cooked dish and whatever ingredients you have around.
The basic steps are the same, but the results are varied and quite tasty.
cooking.stackexchange.com/users/1443/Ocaasi
I think even more important than learning the mother sauces (though they certainly have plenty to teach), is learning the underlying fundamentals on both a culinary and scientific level.
You need to be able to envision how you want a sauce to taste, feel, look and smell (not so worried about hearing) and then translate that into ingredients and execution.
Needless to say this is a lifelong study.
Here's an example of what I mean.
I can think of three major ways of thickening a sauce.
I'm probably forgetting some.
(1) emulsification, such as happens in a vinaigrette, hollandaise, or mayonnaise, in which droplets of one liquid get surrounded by another that can't dissolve it.
(2) starches/colloids which interfere with the flow of liquid, such as cornstarch, flour, arrowroot, or all sorts of fun engineered starches
(3) reduction - simmering out some of the water so the solids are a higher percentage of the volume.
Each of these methods has pluses and minuses.
For example, reduction avoids adding any undesirable starchiness or diluting flavors to the sauce, but requires prolonged cooking or high heat which may change the flavors for better or worse.
I could go on an on!
But the point I'm driving at is, instead of trying to memorize a few sauces, you'll do yourself more good in the long run by learning the principles that they rely on so you are free to create and adapt (and fix when things go wrong).
cooking.stackexchange.com/users/1393/Michael Natkin
The five best candidates would have to be five mother sauces of French cuisine.
These are: Béchamel Espagnole Velouté Tomate (similar, but not to be confused with Italian tomato-based sauces) Hollandaise
Any chef should know these.
These form the basis of many other French sauces.
Some of the more well known include Béarnaise, Mayonnaise, Mornay, and Tartar.
From there you can really expand almost endlessly.
Some of the most well known Italian sauces such as Puttanesca, Bolognese, Pesto, Marinara, and Vodka sauce should be required knowledge as well.
I suggest reading up on sauces on Wikipedia , there are lots of examples there.
cooking.stackexchange.com/users/60/hobodave
There are 5 French "mother sauces": Bechamel - milk, thickened with a roux Veloute - light stock, thickened with a light roux Tomato Espagnole - brown stock, thickened with a brown roux Hollandaise - an emulsification of eggs and butter
They're called "mother sauces" because most (all?)
other sauces in French cooking are derived from these basic sauces.
Learning the technique for a roux is a critical first step in making most sauces.
cooking.stackexchange.com/users/2047/Bob
After the ones that Bob mentioned, other 'worth knowing how to make by memory' are basic proportions and techniques for for : pan sauces (ie, deglaze the pan, reduce, maybe add some butter) mayonaise pesto (and for the most part, 'brown gravy' is a veloute, 'white gravy' is a bechamel, although the fat used for the roux would change)
cooking.stackexchange.com/users/67/Joe
I'd like to learn to make some sauces and I'm looking for the most common, "standard" sauces that professional cooks all learn how to make in culinary school.  What sauces form the basic "building blocks" of cooking and how are they prepared?
What are the fundamental sauces that every cook should know how to make?
cooking.stackexchange.com
<sauce>
cooking.stackexchange.com/questions/4402
cooking.stackexchange.com/users/103/Jason Punyon
You need to be able to understand how a sauce should taste, feel, look and smell, as well as the way that the ingredients combine to create the right texture using emulsification, starches/colloids and reduction of the liquid content. The standard sauces include bechamel, velouté, tomato sauce, bolognese, pesto, marinara and puttanesca. To be able to create these, you can to master the skills of emulsification, thickening and reduction.
You need to be able to envision how you want a sauce to taste, feel, look and smell (not so worried about hearing) and then translate that into ingredients and execution.
It is important to visualise how you want a sauce to taste and then translate that into ingredients. The basic skills are emulsification, thickening and reduction. The standard sauces include bechamel, velouté, tomato sauce, bolognese, pesto, marinara and puttanesca.