Actually, I should clarify. With Class A you have 16.7 million possible hosts (256 * 256 * 256), but with Port Address Translation, since TCP and UDP port numbers are 16 bits long, you'd "only" be able to have 2 ^16, or port numbers 0 through 65,535, thus "limiting" you to 64,000 or so devices on your home network.
Aw crap!!! That changes everything!!!!