Originally posted here by InfiniteL00p
It also really depends on what type of router you're talking about. The common home systems (gateways, etc.) are usually administered via a web-like interface on port 80 or 8080, and usually only from inside the private IP range (192.168.x.x). If remote administration is turned on, only then can an external IP admin it.
l00p
Although there are not quite as many routers that have a Telnet-based control panel, there are still many routers out there that use a telnet-based CP. Doing a little research, I found that some routers even have an FTP-based CP. However, most home routers use web-based authentication for the CP. I have run into many routers that can be controlled remotely over the years, most of which have the SSID of "linksys" and the password of "admin"