DropBox it's the obvious one, but with limited space if you are using the free model. Yes you can earn more space by referring people (500mb each). I have no reason to fault this app, I use it to sync my photos from the phone as I take them.
This cloud backup is the only one I know of that will actually back up your app data. (must be rooted to back up to cloud) So you won't lose your saved games and such. It does however only work on devices with android 4.0 and higher
Just started with this one, not as much space off the bat, they do give space for referrals. The app itself can be set to automatically back up contacts, call log, messages, system settings.. pretty much seems to cover everything except actual apps
I have this on my computer, it came with 20gb of free space, I do have a complaint though, Box is behind the times, there is no ability to sync subfolders automatically. It can make for a lot of dragging and dropping.