Huzzah! iOS 4.3.1 (at least on the iPhone) is fully jailbroken and does not required tethered boots to maintain the magic. The process, which uses Redsn0w (Mac version/PC version) and a proper version of the firmware for your hardware, is unerringly simple and results in a fully jailbroken device.
Again, iPad 2 owners are SOL so don’t even try. Watch this space for updates on that device.