Hours after Apple (AAPL) published firmware update 1.1.2 for the iPhone and the iPod touch — and even before it was officially available for installation through iTunes — rogue programmers had managed to “jailbreak” the iPod touch, once again allowing unauthorized third-party applications to run on the device. See Erica Sadun’s report on TUAW here.

As of this morning, however, the iPhone still hadn’t been re-jailbroken. That means that, as predicted, iPhones updated from 1.1.1 to 1.1.2 won’t run any of the dozens of applications users have been loading on their phones using one-click installation programs like Jailbreakme.

The firmware update appeared on several Apple blogs last evening. News of the first jailbreak was posted shortly after midnight.

Early users are still trying to pinpoint the advantages of performing the upgrade. The chief improvements seem to be the ability to add events to the calendar and easier access to languages other than English. There are reports of bug fixes and performance improvements, but they haven’t been documented.

Firmware update 1.1.2 comes preinstalled on the new iPhones that go on sale in Europe today. If you already own an iPhone, you can download the update here. And although iTunes doesn’t recognize its existence yet, the iPhone can be forced to install the update. Here’s how: After downloading 1.1.2, connect your iPhone to your computer, find your iPhone in iTunes, hold down the option key (on the Mac; Windows instructions may differ), click on Check for Update, and open the downloaded file.

The update takes about five minutes to install, after which any apps you have added will have disappeared — for now, anyway.

[Image courtesy of Engadget.]