1. With Dropbox running, call up the app's preferences. In version 3, you can find them by clicking on the Dropbox menu bar icon and using the gear menu at lower right.
2. On the General tab, uncheck all the following:
"Show desktop notifications."
"Start Dropbox on system startup."
"Enable Finder integration."
3. Close the preferences and restart your computer.
You should now be able to remove any Dropbox file or folder with no trouble. My own way was to use TinkerTool to show all normally invisible files and folders, then to search for "dropbox" with EasyFind and use its contextual menu to "Reveal in Finder."
Lesson: Think twice about installing an app that doesn't supply its own uninstaller. (And there's no real reason to install the Dropbox app anyway, since you can easily upload and download your files from the Web site.)