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.
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)
Super Backup & Restore - Super Backup & Restore app allows users to backup all their stuff such as pictures, videos, apps, text messages, contacts, call history, and calendar data, etc.
i-FunBox - General file management software for iPhone and other Apple products
Droid Transfer - Save and Print your Android Phone Messages, Manage Photos, Music and other files on your Android Phone through your PC. Android Transfer Software.
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.