UPDATE 09/05/2013 – new features are coming soon, such as mutilple site collection backup or scheduling. Stay tuned
As you may already know, there is no way to backup by yourself your SharePoint; it’s Microsoft team charge’s.
However, in some case, this may be a good idea to have a backup of your SharePoint Online content; for example, if you want to stop your Office 365 subscription (reversibility).
So, currently, the only way to get a backup (or get back on premises) from SharePoint Online is either to use a SharePoint migration tool which supports “hybrid” mode (online and on premises) such as AvePoint, or to ask Microsoft team to provide you a backup but… 
Hopefully, someone think about that and there is now a third party solution to backup your SharePoint Online content: this called LeapBackup – see https://www.leaphq.com
You can try it for free for 1 month.
Backup your SharePoint Online Content
This first is to create an account which requires your SharePoint URL, an Office 365 which has access to SharePoint
Then you can perform a backup, but before you need to subscribe for the 1 month free trial – this requires a PayPal account (personally, I don’t like PayPal and always prefer to avoid this)
So once you have subscribed for the free trial, you can do you backup by hitting the Start backup button; off course the time needed depends of the size of your site
For about 1 Go of data, it took about 15 min to complete
The backup process created a temporary document library which is used to stored temporary backup files and will be deleted once the backup is finished
In order to make the backup successful, you must have at least 50% storage available for your SharePoint site collection; if not, just increase the storage quota from the SharePoint Online Administration Center.
NOTE this tool can not backup public SharePoint Online site. At least when I tried it for writing this post.
Restore Your SharePoint Online Content
So, once you have done a backup, you can:
- restore your content
- download the backup files
Just open the Backup tab from the left menu and expand the backup operation you want to restore/download by hitting the Expand link shown below the backup operation
If you want to restore, just click on the Restore button; if you want to download the backup, just click on each file names (don’t forget to download ALL the files)
NOTE backup files are CMP file type for use with SharePoint PowerShell Import-SPWeb command
If you hit the Restore button, you will be asked for a destination URL; for this post, I created a new site collection with a new URL
Do not select a template when creating the site collection
Do not forget to assign correct storage quota
It took about 1 hour to restore this backup
It’s a really simple solution and, better, it is not expensive
NOTE be careful with SharePoint feature when trying to restore to on premises site collection, the backup is coming with all features activated on SharePoint Online – especially these ones SpoGuestIntegration or BPOSExtranetFlag – which will cause errors when using the Import-SPWeb command
To avoid these issue, just change the extension of the main package file to .cab
Extract the content and edit the Requirements.xml to remove these features
Inject the updated file and regenerate a cab file and rename it back to cmp