How do I force Spotlight to index new folders?
From Apple Support: How to rebuild the Spotlight index on your Mac


  
  Choose Apple menu () > System Preferences, then click Spotlight.
  Click the Privacy tab.
  Drag the folder or disk that you want to index again to the list of locations that Spotlight is prevented from searching. Or click the Add (+) button and select the folder or disk to add.
  To add an item to the Privacy tab, you must have ownership permissions for that item. To learn about permissions, choose Help from the Finder menu bar, then search for “permissions.”
  From the same list of locations, select the folder or disk that you just added. Then click the Remove (–) button to remove it from the list.
  Quit System Preferences. Spotlight will reindex the contents of the folder or disk.
  


Note: Apple Support Document Update: Published Date: Nov 14, 2016 See edit history of this answer to see a previous version of this information.



Note: Dropbox specific information as an addendum to the Apple Support directions.

The above directions are the written ones from Apple Support however with an object like Dropbox on the Sidebar in Finder do not drag and drop it from there, instead either add it to the Privacy tab using the plus ("+") button or drag and drop it from your Home folder.  Then remove it using the minus ("-") button.

If Dropbox was removed from the Sidebar in it can be dragged back from one's Home folder.