I use dropbox but it isn’t my main sync app. Dropbox doesn’t give you the option to remove the icon from File Explorer, and if you manually remove the registry entries that are related to it, they are recreated at each automated update of Dropbox.

Another way of removing the icon is to add an entry to Windows “NoEnum” registry key. This tells Windows to not process matching keys, so Dropbox just gets ignored.

Add the following registry entries:

Download reg file
  dropbox-removal.reg (476 bytes, 2,240 hits)