There are many ways of backing up data from your Android phone, but none of them come close to Clickfree's ease of use. Clickfree Mobile Backup is a free app that lets users back up their Android data on multiple cloud services, including Dropbox and Box.net.
There's also a Pro version of the app that features scheduled backup, which is very important, and ad removal. Google has built in a backup feature in Android 4.0 and later, but it doesn't let you choose where your data is going.
I lost all of my data once. It was a traumatic experience that turned me into the miserable man that I am today. If you don't want to end up like me, get Clickfree on Google Play today.