Pangu's new iOS 9.2 - 9.3.3 jailbreak
This jailbreak is only for 64-bit devices. 32-bit devices are not compatible with this jailbreak tool.
The following devices are compatible:
iPhone 5s
iPhone 6
iPhone 6+
iPhone 6s
iPhone 6s+
iPhone SE
iPad Mini 2
iPad Mini 3
iPad Mini 4
iPad Air
iPad Air 2
iPad Pro (both sizes)
iPod Touch 6G
This is a semi-untethered jailbreak
After rebooting your device, your tweaks will not function and your device will appear to not be jailbroken. To fix this, open the PP app.
Official jailbreak download
Download link: http://pro.25pp.com/ppghost
Direct link: http://ghost.25pp.com/soft/pppc_setup/pphelper_5.0.3.1154_25pp_00121_Setup.exe
Checksums
Use these to ensure that the utility you downloaded is legitimate.
SHA1: 0b836788bf9cd385b187e201480519394caf4dc2
MD5: 9caf01432e77da9ea22bc943e3b67d62
SHA256: 62d6489957dc6d8912a4cfbbe695439a8d53ee02b694f837363e500e1c8b8195
Jailbreaking instructions
Advice for upgrading from jailbroken device
Write down a list of your favorite packages, or export a list using AppInfo or similar - try Appster or Capture View. (Technically you can try a whole-package-list backup tool like PkgBackup, but see step #6 for why you might not be happy with the result if you use that.)
You can also go into Cydia and take screenshots of your installed apps and repos. If you do this before your backup they should still be on your device after you restore. If you're paranoid (like me) you can email them to yourself or copy them someplace else for safekeeping.
Do a full backup of all your data with iTunes or iCloud (or your preferred method).
Download the latest iOS 9.3.3 IPSW file from https://ipsw.me. (this is done instead of an OTA update to reduce the chance of encountering problems)
In iTunes, shift-click (alt-click on mac) on "restore" and choose the ipsw file you downloaded in step 3. (Side note: using the "update" feature will lose some disk space on your iDevice until your next full restore.)
Run PP Helper and follow the jailbreak process.
Based on your written or exported list of favorite packages, try installing one or a couple of them at a time. It's very likely that many of those packages will have compatibility problems, so it's easier to troubleshoot problems if you don't install everything at once.
After you have finished the jailbreak and have Cydia up and running, here is a getting started guide that you may find beneficial.