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)
greenpois0n - Greenpois0n performs an untethered jailbreak for iOS 4.
iExplorer - iExplorer lets you easily transfer music, playlists, text messages, files and more from any iPhone, iPod, or iPad to a Mac or Windows computer and iTunes.
3uTools - 3uTools is a most efficient iOS file and data management tool for Apple users.
CopyTrans - CopyTrans is a tool for managing the files on your iPhone or iPad through your computer's interface.
Blackra1n - (This is an OUTDATED jailbreaking method.)