Suppose I have a Java application that opens a database connection. Normally I would add a connection.close() in a finally block, but this block wouldn't be executed in the case of a kill operation, or any other abnormal termination, would it? Are there any other precautions that I, as a programmer, can make in order to close the connection properly before the application exits?
You should look at the Runtime.addShutdownHook() method for Java (http://java.sun.com/javase/6/docs/api/java/lang/Runtime.html#addShutdownHook(java.lang.Thread)). It allows you to add a hook that will be called when the virtual machine terminates. You can use it to call a cleanup routine.
That would be for a TERM signal though. A KILL signal will kill the process and not allow it to do any cleanup (because the KILL signal cannot be caught or ignored by the receiving process).