Blackra1n - (This is an OUTDATED jailbreaking method.)
iMazing - iMazing lets you transfer music, files, messages, apps and more from any iPhone, iPad, or iPod to a computer, Mac or PC. Manage and backup your iOS device simply without iTunes. (was DiskAid)
sn0wbreeze - sn0wbreeze is an advanced jailbreaking tool that lets you build a custom IPSW ("iPhone...
iFaith - iFaith is a program that can save the SHSH blobs of the current version of iOS that's running...
unc0ver - The most advanced jailbreak tool.
Absinthe - Absinthe is a tool by the makers of greenpois0n that provides an untethered jailbreak on iOS 5.1.