Android already backs up most of your data. Contacts, calendar, gmail, downloaded/purchased apps, Hangouts messages, etc are all uploaded to the cloud. If you download Google Photos, you have unlimited storage for photo backups. If you use Google Play Music, you can upload 50k songs for free and have it stream or store locally on your phone and the web, meaning all your playlists are synced with iTunes and you don't have to worry about losing them on your phone.
For actual app backups, you should root and use Titanium Backup.