VincentP :
Mainstream Intel CPUs support DDR3 dimms up to 8GB each.
Motherboards for these CPUs support up to 4 dimms, so this allows the maximum 32GB supported by the CPU.
I have read that AMD CPUs support DDR3 dimms up to 16GB each, but I can't find this in AMDs specifications or even a maximum memory specification.
I would follow the specification from the motherboard manufacturer.
Both types of mainstream CPU have two memory channels, you should use 2 or 4 dimms for optimum performance.
Yeah pretty much. Let's do some math.
The highest native density being manufactured for DDR3 is 4 gigabits per DDR3 SDRAM chip. 8 gigabit DDR3 SDRAM chips are available, but these are constructed from two 4 gigabit chips stacked on top of each other. Stacked chips are not natively supported by Intel or AMD, but it is possible to use them if the motherboard manufacturer has altered the chipset's memory reference code (MRC) to support it. As far as I know, only a few vendors have done this. Asus claims that their Rampage IV Extreme and Rampage V Extreme motherboards can support up to 128GiB of DDR3 SDRAM if 16GiB UDIMMs are used.
Anyway, on to the math. This is what the limits look like in the consumer world:
4 gigabits per chip * 8 chips per rank (8-bit IO) = 32 gigabits per rank = 4 gigabytes per rank
4 unbuffered ranks per channel (usually two dual-rank DIMMs) * 4 gigabytes per rank = 16 gigabytes per channel
Multiply that by the number of channels in the platform to reach the maximum installed capacity.
The enterprise world gets substantially more complicated.
32GiB and 64GiB DIMMs are available for use in enterprise platforms. Some of these platforms do support stacked SDRAM chips through the use of a complex intermediary buffer (LRDIMM)