You can give Folder Downloader for Dropbox a shot. I have used it once but have never needed it again.
Simply sign into your Dropbox account, long press on the folder you wish to download and either tap and hold on a folder and select Download folder to
or tap the button at the bottom that says Download all to
which downloads all the files and folders in the folder you are currently browsing (so for example if you are on the base folder, it will download everything in your Dropbox account)
Features
- Signs into Dropbox with the Dropbox API so the app never see's your password
- Gratis with no ads
- Lets you choose what directory to download and where to download that directory (either on the SD card or internal storage)
- Will download the folder recursively (press and hold folder and select
Download folder to
)
- Download is preformed in the background so you can do other things while your folder downloads
- Error reporting and the option to redownload on error
Screenshots of a test run I did (click images for larger variants):
I tapped and held on the folder "Test folder" which has two more folders in it, called "Test folder 2" and "Test folder 3". Then I selected my SD card for the app to download to:

And here you can see that the app successfully downloaded all folders recursively (although I didn't test with files, it will recursively download those as well):
