Accessing external mail servers is forbidden (antivirus policy); only use the internal server to send or receive.
Network games, such as Doom or Quake, are forbidden, except between 8 a.m. and 6 p.m. all weekdays for members of management.
Websites such as playboy.com are forbidden for legal reasons.
Enforcing the first policy without a firewall would be possible, but difficult. In theory, if you managed to secure every single desktop machine and prevent users from installing software, it would be possible. Then you would need to prevent people from attaching "rogue" laptops and so forth to the internal LAN with software preinstalled. While possible, this is a Herculean task compared to configuring a dozen rules (or even a hundred rules) on your firewalls to prevent access to the ports and servers that IRC, AIM and the rest use.
The second policy would be very difficult to enforce without a firewall. You would need to do the above steps to prevent people from installing their own email software or using rogue machines such as laptops with it preinstalled. Moreover, any email software you do use (such as Outlook or Eudora) would need to be configured so that users could not modify any preferences, add new accounts and so on. This is not possible in almost all email clients.
The third policy is virtually impossible to enforce without a firewall. You would need to take the above steps to prevent any user except for management installing the software. One possibility would be to place the software on a network share and only make it available from 6 p.m. to 8 a.m., and on weekends to users of the management group. However, many network games would not function properly, and you would have to prevent the software from being copied off, etc.
Even with all this, the software may still continue to function after 8 a.m. if it is running on the client machine (or it might crash horribly). In any event, this is much easier to enforce with a firewall such as FW-1: enable user authentication, then define a policy that allows users of the management group access to the ports used by these games at the appropriate times.
Enforcing policy number four is basically impossible as well without a firewall. While some Web clients do allow you to list sites that are off limits, keeping the browsers on multiple workstations up to date would be a virtually impossible task. Compare that with configuring the firewall to force WWW access through an application-level Web proxy where *.playboy.com can usually be blocked with one additional line.
Generally speaking, any security implementation done in a network will help with its overall health. Cataloguing systems and software versions to decide what needs upgrading first, implementing automated software upgrade procedures, and so on all helps with the overall health of your network and its systems.
A network configuration that creates chokepoints for firewall deployment also means you can easily implement a DMZ, a zone with servers to handle inbound and outbound information with the public. These servers can typically run a hardened and stripped down OS and application software. A proxy email server, for example, only needs to be able to accept and send email. There is no need for user accounts, POP or IMAP services, or GroupWare software integration.
Usually the simpler a system is, the easier it is to secure, and hence the harder it is for an attacker to break into. Securing a messy network is almost impossible. You must find out what you have, which versions, where the servers are deployed, what network links exist, and so on.
Firewalls, properly deployed, configured, and main