What's the correct number of workers to put on gathering vespene and minerals in StarCraft 2?

In StarCraft 1, I didn't halt worker production until I had 3 for every 2 mineral patches, and 3 for each vespene geyser. This was my own personal guideline, and I have no idea how efficient/wasteful it was.

What's an appropriate guideline for maximum income rate in StarCraft 2? Does it differ by race?

I know some people have answered this but I thought I could add a little data.

For gas, full saturation is 3, however the third isn't worth as much as the first two. As a result its worth getting a second geyser before putting a third worker on the first.

This is also true for minerals as shown by this graph:

As you can see after your first 16 workers the gain per worker starts to decrease dramatically. As a result when you start an expansion you should shift any excess workers (over 16) to the new expansion.

The original research can be found in this paper: Worker Income Efficiency in Starcraft II By Chet 'Cheticus' V. The paper reports original data collection and methods, as well as the formula's uses for the 'least squares regression.'

Same values: 3 per gas, 3 per patch. I think that the in game tips also say that, but I got that info from looking at high-level replays.

Some players prefer less, though, for various reasons - less wasted supplies, for example.

3 is what is necessary to "saturate" a patch or geyser.

However, I like to play with about 5 for every two patches or so and 3 on each geyser.

This almost maxes out gathering speed, wastes fewer resources, and scales nicely when a patch is exhausted.

Since SC2 is much more economy based than SC:BW the golden rule is never stop producing workers!
If you get much more than 3 per patch: EXPAND and do a miner-slide (moving workers from main to expansion).