Since the release of OS 3.1.2 last week, there has been a friendly competition to release a jailbreak for the iPhone 3.1.2. GeoHot was the first to release the iPhone 3.1.2 jailbreak called BlackRa1n, followed by the Dev Team and their PwnageTool.
This article is a summary of the options you have to jailbreak your iPhone 3.1.2 depending on your model.
There are many reasons to jailbreak your iPhone 3.1.2 such as being able to install application not allowed in the App Store, or most importantly, to unlock your iPhone so it works with other carriers.
Jailbreak iPhone 2G 3.1.2:
Jailbreak iPhone 2G 3.1.2 with BlackRa1n RC3