iOS/Windows: The jailbreak for iOS 7.1.1 has been released. The jailbreak tool, called PanGu, is Windows only, but should work on every iOS device.
The the installation process isn't as simple as the previous jailbreak, but this Reddit thread guides you through the process if you need it. It does install a piracy store that you'll probably want to remove (just uncheck the box during installation).
Most of the jailbreak community has given the jailbreak the go-ahead, but since it's from a new team and still a bit untested, we recommend holding off for a while until it's confirmed to work without bugs or anything malicious hidden inside. That said, if you want to go ahead, you can snag the software from the link below.