oandbackup - Make backups of selected apps on your device and restore from those backups.
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.
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.
PhoneDog Phone Transfer - Transfer data from iPhone, Android, iOS, and Computer to Anywhere without any loss with FoneDog Phone Transfer. Such as photos, messages, contacts, music, etc.
CopyTrans - CopyTrans is a tool for managing the files on your iPhone or iPad through your computer's interface.