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)
Titanium Backup - Titanium Backup is a very old backup app that has been around since the early days of Android. In fact, it's one of the few apps that covers all versions from 1. Read more about Titanium Backup.
checkra1n - Jailbreak for iPhone 5s through iPhone X, iOS 12.0 and up
Wondershare MobileTrans - Wondershare MobileTrans is a 1-Click Phone to Phone Transfer for you to move data between devices with different operating systems. Your must-have phone Transfer.
Blackra1n - (This is an OUTDATED jailbreaking method.)
ApowerTrans - Transfer data from a phone to another phone.