How many colors did the "Old Master" painters really use?

Question

For example, Da Vinci, Rembrandt, Van der Weyden, perhaps Van Gogh as well. 

Did they all use the standard colors and then would be mixing them to achieve different shades? Or perhaps some of them were using a great variety of uniquely different colors?

Answer 1

They each had a limited amount of colors(pigments) to work with.
The amount of color pigments available depended most on availability and also on price.
In 1841 the paint tube was invented, so artist could buy ready made paint.
Before that time the artist had to make their own oilpaint from pigments they bought.
So only Van Gogh could buy his paint, the others had to make their own paints, or used their apprentices to do that particular job.

They all mixed their standard color paints to get the shades they wanted.

Answer 2

I don't think anyone has ever scientifically analysed every single shade and tone of every single of the thousands of the works of artists who have existed since before the ready-mixed tube paint was developed. There is, however, plenty of analysis of the different pigments. The National Gallery in London certainly has made a number of publications and papers in magazines in the past on this very subject (the Scientific Department) as study helps the conservation of old works.

All artists would have made, or had their apprentice make, their paints from the basic earth and mineral and plant pigments, and then mixed according to their own palette preferences.

So yes - standard colours (basic ground-down pigments) and then mixed. And no, I don't think any 'unique' pigments, although you may find some differences in, say, Asian and Western and Australasian art, where the import or export of materials was not possible in previous eras.