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.