There's been a release of a new jailbreak for those with any iDevice on iOS 6.0-6.1
DOWNLOADS AT THE BOTTOM OF THE GUIDE.
UPDATING TO 6.1 METHOD
1. You're going to need to download the iOS 6.1 IPSW from iTunes and update your iDevice if you're not already updated(If you are already updated skip to 2) and download evasi0n.
2. Once updated, create a backup of your iDevice, and disable your lock code if you have one. You're also going to want to disable auto-sync in iTunes. If you don't know how to do this all you have to do is "Edit -> Preferences... -> Devices -> Check 'Prevent iPods, iPhones, and iPads from syncing automatically'".
3. Now that's done, restore your iDevice as "Set up as new Device". It is NOT recommended to restore from a backup at this point.
4. Close out of iTunes/XCode when the device is restored and open the evasi0n program.
5. In evasi0n just click "Jailbreak" when your device is recognized. Let it go through the process and do what it says on the program.
6. Open iTunes when the jailbreak is complete and restore your device using the backup you made earlier!
7. Voila! You now have the latest untethered jailbreak on your iDevice. Enjoy!
ALREADY ON A TETHERED JAILBREAK?
Well, you're in luck!
1. Search Cydia for "evasi0n 6.x untether" and install the package!
Congrats, you're now on an untethered jailbreak. Enjoy!
evasi0n mirror - WINDOWS
evasi0n mirror - MAC
evasi0n mirror - LINUX
WARNING: CYDIA IS VERY SLOW AT THE MOMENT DUE TO THE LARGE CAPACITY OF USERS.