While there was always a relatively quick solution for previous iOS versions, the untethered jailbreak is still missing for iOS 6. Although there are various rumors and reports that an iOS 6 jailbreak could be released in December, there is no concrete information yet. Apple is already working on iOS 6.1, which is currently available as Beta 3 - if there would be a jailbreak for iOS 6.0.1 now, the work with iOS 6.1 would have to start all over again.
Jailbreaks are popular for Apple devices such as the iPhone 5 or iPad 3, as they allow software to be installed from alternative sources such as the Cydia store, and provide features that Apple has not implemented. Apple tries to protect the system as good as possible against jailbreaks, but this has not always worked in the past.
As soon as there are news about a working iOS 6 untethered jailbreak that also supports the iPhone 5, there will be an update here of course - for my iPhone 4 with iOS 6.0.1 a jailbreak would be worthwhile, too.