In The Matrix, humans' body heat is used to power the machines, but it was hinted at in a comment on another question that the machines used human brains for processing power. Is this claim substantiated by anything?
Nowhere in the films or the Animatrix is it even hinted that the computing power of humans is used in this fashion. The only side effect of protecting themselves from the humans is a bit of juice the machines get back from the humans.
Although human brains are capable of some interesting computations (that are hard to express in machine-lingo), it would be really hard to emulate a platform on top of thoughts that would support a generic operating system, let alone a sophisticated A.I. If the machines don't use humans to run themselves, any computation they would need (for industrial reasons, for instance) would be easier to be computed by a machine than this human-computer-abomination.
Unless, however, you subscribe to the Matrix in a Matrix theory, where "the humans" (Trinity, Morpheus, ...) are actually programs that are being controlled by humans outside the "real-world-matrix". Then you could argue that they use the processing power for computation (or train the A.I.).
Yes, this claim was made in the Webcomic "Goliath" by Neil Gaiman. It's pretty clear from the text that the agents view their human captors as not only a power supply but are also using them as CPUs and/or spare memory capacity.
Note that while the Webcomics are largely viewed as canonical (due to the extensive involvement of the Wachowskis in their writing and selection), Goliath is pretty far off the beaten path and probably contains non-canon elements.
"What's going on?" I asked. "Do you know?"
"Enemy missile took out a central processing unit," he said. "Two hundred thousand people, hooked up in parallel, blown to dead meat. We've got a mirror going of course, and we'll have it all up and running again in no time flat. You're just free-floating here for a couple of nanoseconds, while we get London processing again."
I made the mistake of telling Susan some of what I believed one night - about how none of this was real. About how we were really just hanging there, plugged and wired, central processing units or just cheap memory chips for some computer the size of the world, being fed a consensual hallucination to keep us happy, to allow us to communicate and dream using the tiny fraction of our brains that they weren't using to crunch numbers and store information.
"We're memory," I told her. "That's what we are. Memory."
In one of the DVD sets' extra material there is an interview with Lana Wachowski, in that interview we learn that in the original version of The Matrix script the humans were not used as a heat source, they were indeed used for computation.
She explained that one of the suits told them to change it, when asked why they didn't refuse she said "it wasn't that important to us, it was just a plot device".