Yes, you need a router. The Xbox 360's wireless adapter (or built-in Wi-Fi on Slim models) connects to a wireless network created by a router. The router is the gateway between your home network and the internet. The connection chain: your ISP provides internet to your home, the router distributes it via Wi-Fi or Ethernet, and the Xbox connects to the router's Wi-Fi (or via Ethernet cable). Without a router, there's no network for the adapter to join—a modem alone typically provides only one wired connection.