We lost connectivity while configuring a router interface we had telnetted, requiring us to get physical access via a console cable. Additionally, if remote offices are connected via ISDN, DSL or cable and receive dynamic addresses, the only way to manage them remotely is through an external, analog modem. Although access via a modem is not the speediest route, it will get you through when all other connectivity goes down. Don't be chintzy with a bargain-brand internal modem, which is good for surfing but requires the PC to be running. Plus, you will have to have a server ready to make the connections for you.
Most routers have external comm ports available for dial backup.
Sticking an external modem on one of those ports makes sense. As long as the router and modem are on a UPS, chances are good you can still connect even when the power is out. Pick up a good external modem, such as a U.S. Robotics Courier External V.Everything or similar model. The Courier is a good choice because of the wide variety of protocols it uses and its external DIP switches, which can be used for configuration. Some network equipment, such as Cisco Systems and 3Com Corp. routers, can configure a modem through a script, so the requirement for hardware configuration is not as pressing.