If a series of computers are connected to the internet via a router with a built-in firewall, is the presence of a software firewall on each machine necessary or just a needless redundancy.

Here's the scenario: A network of 7 computers is connected to the internet via a D-Link DI-704P router with a built-in firewall. One linux machine acts as a web server and ftp server, another linux machine serves a battle.net gateway, and the other machines are more or less just mixed OS, local user desktop systems. There are no computers setup in the DMZ, all are behind the firewall. Is this D-Link router doing the job of preventing access to the network via its firewall, or is it necessary that a software firewall be configured on each machine or is this essentially useless?