Hello,
I have live video coming in via webcams, and I would like
for each frame) to know some aggregate data such as
the average brightness and (if possible) the maximum,
minimum, standard deviation (OK I am dreaming here).

Alternatively, a histogram of brightnesses from which
I think I can extract the statistical information myself.
Is there some node that gets this kind of information
from a VideoTexture?

there is no built in node in vvvv that calculates the histogram of a videostream. but if you’re only a bit into programming it should be rather easy to write a freeframefilter that does exactly what you want.

in case you dont need to need to calculate the precise measurements, Pipet is an easy way to go. Key idea is using only a subset of all pixels, perhaps a random set or grid of 100 pixels to calculate your aggregate data.

Use RandomSpread or LinearSpread and Cross to define some point coordinates. use Pipet to get the Color of the Video at these points. Use HSL (Split) to get the brightness. Use Bounds to get maximum, minimum and average. From that some simple artithmetic nodes will get you easily things like standard deviation - no dreams required, just basic math.