The Chronic Dev Team has released Absinthe 2.0, an untethered jailbreak for almost all devices running iOS 5.1.1. After the first version still caused some problems, there is now version 2.0.2. The jailbreak works - as usual with newer tools - very easy. First create a backup, then reset the device (as this speeds up the process), start Absinthe and trigger the jailbreak and then restore the backup.
The following devices are supported: iPad 1, iPad 2, iPad 3iPhone 3GS, 4/4S and the iPod Touch of the 3rd and 4th generation. After the Jailbreak you can install additional apps not released by Apple via Cydia.