Apple recently released a 10.5.6 update to OS X. While I was downloading the new stuff using Software Update, my internet connection was interrupted. I relaunched Software Update and assumed it would continue downloading. It appeared to finish and then asked to reboot to complete the update process.
Unfortunately, the update process got stuck on Configuring Install and just sat there indefinitely. After an unhealthy hard power reset, I tried again with no luck. It seems the interrupted download led to some incomplete files and was hanging the update process.
I was able to solve the problem by deleting the partially downloaded files, then re-downloading using Software Update. This time around, the update applied successfully, upgrading and patching my OS X installation.
Hopefully this post will help others experiencing the same problem. My initial Google search returned a lot of outdated results.
In summary: if you keep getting stuck on Configuring Install during an update, try deleting the files in
/Library/Updates/ and restarting the update process.