Is it necessary to back up Dropbox contents?
Any time the question of Dropbox comes up, I have to restate one key message. If you are in an enterprise, work with your IT team about the use of Dropbox or any other collaboration tool that uses a public cloud storage repository. If your IT team has authorized its use or if you ARE the IT team, then you need to determine if and how it should be backed up.
At Storage Switzerland, we use Dropbox, since most of our data is going to be published publicly anyway. We do, however, encrypt sensitive data. From a protection/recovery perspective, Dropbox provides some basic tools, like version tracking and undelete. You can also subscribe to their "packrat" service that will keep versions of files almost indefinitely.
We suggest making a backup copy of your Dropbox data even if you are a packrat subscriber. Why? Mostly, it is for 'just in case' situations. Public services are prone to mistakes just like any standard IT department. Outages at Amazon and others have been well-documented. You don't want your data to be the casualty of some broad failure or denial of service attack.
Personally, I have a product that synchronizes my Dropbox folder to a RAID protected network attached Drobo 5N. Each quarter, I redirect that data to a different directory. For example, right now it is going to "DB Backup Q2-2013." This gives me some historical archive, in addition to simple data protection. Also, as a result, I don't pay extra for their packrat service.
In addition, my laptop is backed up to a different device daily. As part of that backup, my Dropbox folder is protected again. Finally, and mostly because I am paranoid about data loss, I also have that data copied to an RDX (removable hard disk cartridge) once a quarter. That RDX is stored off-site.
While you don't have to resort to the same levels of backup redundancy that I have set up, some additional layer of protection of Dropbox is a must, in my opinion. That can be a secondary sync, a standard traditional backup that includes the Dropbox folder, or a periodic copy to an external device that goes off-site.