A jailbreak for iOS 8.0-8.1 has just been released by Pangu, surprising most of the jailbreak community!
Currently still in early stages, requiring the user to install Cydia separately after jailbreaking, but Pangu should incorporate Cydia into its next release, very soon.
Keep in mind:
- Currently only available for Windows (Mac version to be released soon)
- Most jailbreak tweaks will not work on iOS 8 yet, as mobile substrate still needs to be updated
Tutorial to install jailbreak and cydia:
http://www.idownloadblog.com/2014/10/22/how-to-jailbreak-ios-8-1-with-pangu-1-0-1-video/
If you're new to the jailbreak scene, I'd probably recommend waiting till the next version of the jailbreak tool with Cydia integration so it doesn't need to be installed separately (hopefully within the next couple of days).