You don’t need to install drivers, therefore less hassle and it will work with OS.
Provides a hardware firewall, so you don’t need to install a software FW.
You can connect multiple computers (if you get a multiple port router, but most routers have at least 2 ports)
You can use P2P applications(torrents, eMule etc..) on multiple computers. If you use a modem and a basic switch to share the connection then you can only use those apps on the machine with the modem.