sudo rm -r /Library/DropboxHelperTools/ \
/Applications/Dropbox.app/Contents/Resources/DropboxHelperInstaller.tgz

Then use Force Quit to restart Finder.

This doesn't seem to affect the operation of the magic ~/Dropbox/ folder.

It comes back sometimes -- possibly whenever Dropbox auto-updates as new version of itself? So you might need to do it again. I put it in cron.

Why:

I upgraded to the new 1Password and it seems to have pulled down a new version of Dropbox as well.

Dropbox, in their infinite wisdom, have decided that your Finder context menu should now have a "Move to Dropbox" menu item right where "Move to Trash" used to be. Not at the bottom with the other Services items, but right up top. Third item on the menu. Where my Trash muscle-memory is.

The technical term for this is "a dick move".

The way you're supposed to add things to that menu is by putting an action in ~/Library/Services/, which puts things at the bottom of the menu, but I guess being at the bottom wasn't enough of a billboard to advertise their app, so instead they did it through some kind of dynamic-loader-injection exploit.