Some people (myself included) have several computers running Linux connected to one UPS. One computer monitors the UPS and needs to get the other computers to shut down when the power goes out.
We assume the computers can communicate over a network. Call the computer that monitors the UPS the master and the other computers the slaves.
In the old days this required some fancy programming.
These days, the best thing to do is to pick up either the powerd-2.0.tar.gz package or the upsd-1.0.tgz package (see section Software), and follow the instructions. Both are able to run on the slaves in a mode where they connect over the network to a powerd or upsd process running on the master to query the status of the UPS. Some of the APC specific packages seem to have this ability too.
Note, though, that if your network is insecure, you might want to add a little security to this, lest someone spoof the slave powerd processes into thinking that the power is out.
Another possibility is to go for SNMP (Simple Network Management Protocol). Detailing the use of SNMP is beyond the scope of this document, not to mention currently being beyond me.