Xavier Media

This plugin will do a backup of your WordPress database and, or your files in wp-content/uploads and saves 
it somewhere safe. You can have the backup saved in your <a href="http://db.tt/9Jo39Xy" rel="nofollow ugc">Dropbox account</a>, a FTP account of your choise, your 
account with <a href="http://www.securepaynet.net/email/online-file-storage.aspx?ci=1796&prog_id=xaviermedia&isc=xmbackup" rel="nofollow ugc">Online File Folder</a>, or have the backup emailed to you (not recommended for large files). You can 
select to have the backups named the same every day or to have a date added to each file name.
This plugin requires PHP, cURL, PHP compiled with ZIP support, and Oauth (for Dropbox).
** NO WARRANTY SUPPLIED! **
** Make sure you test your Backups! **

XM-Backup

Does a backup of your Wordpress database and, or your files in wp-content/uploads and saves it in a safe location.

acespritech

Are you looking for a way to create an upload form that automatically sends WordPress file uploads to your Dropbox? Using this Plugin you can easily integrate your Dropbox to your WordPress website. You can select maximum file size till your dropbox maximum upload size.
Features:- 
1 – Easy to connect form with Dropbox. 
2 – There is no file limit for upload. 
2 – Admin have short-code of form to display form in any page using it.
Shortcode:- [aspl_dropbox]

ASPL Dropbox File Upload

Another Best Plugin for Integrate Dropbox With Your Upload Form.

XM-Backup vs ASPL Dropbox File Upload