This also depends on the cable modem, the cable company, and the router. I use Comcast HSI and I made the error of telling them I wanted to hook up several computers to the internet. So they had me get the "networking kit". It worked out in the end, as the modem/router is pretty good, plus it only cost $5 more per month. But I am only allowed 5 IP addresses. And the modem/router is set up as the DHCP server, I can't change this setting. So, bottom line, I can still only connect 5 computers regardless of what router I use since the modem/router sets the IPs. You can (should) have only one DHCP server per network.
You also need to be sure that the cable modem you buy is going to be compatible with your cable provider. So providers have requiremetns that must be met by any "3rd party" modem you use.
\Dan