Does the Xbox 360 come with a router cable?

If you count a router cable as a ethernet cable, yes. An ethernet cable is what you plug from your xbox into a laptop/router/modem to connect to xbox live.

The following SKU's come with ethernet cables.

*Xbox 360 PRO

*Xbox 360S

*Xbox 360 Elite

The xbox 360 CORE and ARCADE have no ethernet cables.

Hope this helped.