The Dropbox client has some issues, when installed on the brand new Ubuntu 13.10 Saucy Salamander. The sync works properly, but the user is not allowed to access the Dropbox GUI and the indicator is missing. This may be caused by the latest update of Unity 7, which does not fully support Dropbox yet.
In order to fix this issue, all you have to do is update the system and install the libappindicator1 package. Like this:
$ sudo apt-get update
$ sudo apt-get install libappindicator1