Calculate how much testing will have to be done (as time, say you come up with a figure of 200 hours), then figure out how much time a single tester would spend on the task, and you have a figure for the number of testers you need.
Of course that should take into account retesting bugs they report, duplication (especially with volunteers testing games), people not actually doing the work they sign up for (especially with volunteers testing games, many just want to play something new and shiny before anyone else, and get a free copy at release date as a reward).
There's no magic number, depending on the size and complexity of your system, the number could be anywhere from two or three people (you do want some duplication of effort, to cut chances that someone misses something) working for a few hours over a weekend to dozens of of people working full time for months.
And with consumer products there's the added factor of disparate hardware/software combinations it will run on. It wouldn't do to test a graphics heavy game for example on only 2 computers, both with the exact same videocard, operating system, and drivers.
It will need to be tested on a broad range of hardware/software combinations to determine if it works properly on all of them (or at the very least to be able to mention in your documentation what the hardware/software requirements are to run it).
All of this is true for both games and any other system (and not just for software either).