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.

Blighty

This plugin allows the complete file structure of a folder in Dropbox to be shared within a WordPress page or post. The folder can then be navigated via the WordPress site and files selected and downloaded. Changes in the Dropbox folder, such as the addition or deletion of files, are reflected through to the WordPress site.
<h4>Features</h4>
<ul>
<li>Shows a folder/file navigator that mirrors a folder in your dropbox account.</li>
<li>Optionally display file size and file date in the folder display.</li>
<li>Allows for file uploads, either to a dedicated hidden folder, or to the currently displayed dropbox folder.</li>
<li>Allows access rights to be set on each top-level subfolder.</li>
<li>Compatible with most lightbox-type image plugins.</li>
</ul>

Blighty Explorer

Allows the complete file structure of a folder in Dropbox to be shared and navigated within a Wordpress page or post. It also allows for file uploads.

ASPL Dropbox File Upload vs Blighty Explorer