Ability to network PC's.
As you have a printer server, the ability to share a printer between your networked PC's.
Can connect more than one PC to a broadband connection at once.
No need to "dial-up" as connection always-on.
Routers are more suited to the new up to 8Meg products than USB modems as disconnecting/reconnecting can confuse the BT monitoring kit and cause speed problems.
Many routers have built-in firewall for added security.
There's probably tonnes more I haven't thought of.