Demon dialing was made famous in the movie War Games, in which the protagonist sets up his phone to call every phone in another state until he reaches another modem, from which he can crack into more systems.
Similar to demon dialing is a port scan under TCP/IP, which "dials" every TCP port of every IP address to find out what services are available, then attacking them by guessing passwords or by exploiting vulnerabilities in software that runs with elevated privileges.
See also: war dialing, war driving