Often very convenient feature would be ability to run Dropbox application in background system service mode, not stick to particular login session context. Currently, only running Dropbox as a regular application is supported. Would be no so hard to support for additional tools for running the application in a service context. This doesn't imply any change in the existing application! It could be used as is. Very often this mean just some additional system scripts (for linux install, for example, especially useful for headless install), nothing more.
In such a way Dropbox work can continue even after no any user logged in a particular machine, used as a server. This would be useful for all supported platform - Mac, Linux, and Windows.