The Evasion jailbreak for iPhones running iOS 6.x was patched up real well by Apple in iOS 6.1.3—but now, a dev has managed to finally crack version 6.1.4 on the iPhone 5.
iOS 6.1.4 rolled out in May for iPhone 5 users, offering bug fixes and stymying jailbreaks. But developer Winocm now has iOS 6.1.4 running Cydia on an iPhone 5. Details are pretty thin on the ground, but Winocm has at least uploaded some of the code required to make the jailbreak work for iOS 6.1.4, and forums seem to suggest that some people have successfully managed to use it.
Sadly, though, it's quite an involved process: you'll need to wrangle with your own kernel exploits, as well as using Wincom's code, to jailbreak your iPhone 5 with iOS 6.1.4. One for the more technically minded, then. [Redmond Pie - Thanks, George!]