In the case of Borland's Interbase (now called Firebird), there was a hidden super-user that the system required in order to work. This hidden super-user could not be disabled, and it had a known password that could not be changed (until a patch became available to do so). This would allow anyone who knew the hardcoded username/password combination to access any installation. Disabling this account breaks the system because it can no longer authenticate users.
CERT advisory on Interbase.
Is it as simple as the the program going out and checking a web service and disabling itself?
This is generally how many forms of license management work. Some simply check to see if "my serial number" is in use, and if so, they exit. Some use a form of PKI and revoke local certificates if the license is invalid. For example, Adobe Reader pings crl.adobe.com when it starts to see if any licenses have been revoked, as the key to enable plugins to work in the free reader require a digital key. If a plug-in does things that violate the licence, the cert enabling it will be revoked. License management is a very complicated process because you've got to stay one step ahead of the crackers, and even minor bugs in your licensing code will cause major customer problems.