syncing a Dropbox to a linux server?
Unfortunately the above link posted by @reefnet_alex is no longer accessible. The new Dropbox Linux client works perfectly on headless / UI-less machines, though.
https://www.dropbox.com/install?os=lnx
There is step-by-step post here: http://www.dropboxwiki.com/Text_Based_Linux_Install
Is this what you're looking for?
http://www.dropboxwiki.com/Text_Based_Linux_Install
I run Dropbox in KDE, so I was aware there's no need for the Gnome dependencies, and this article covers installing Dropbox on a text based linux install. This would be an excellent way to allow a client (in the person sense not the software sense) to upload files to a server without footering around with FTP or the like (how many clients actually get FTP?!). Throw it in your Dropbox folder, there it is on the server. Bish bash bosh...
First question would be does your hosting company actually allow you to operate a long running userland daemon? Dropbox consists of a proprietary userland daemon and an open-source client. If your hosting account can't run the daemon then it will have problems remaining in sync.
The second problem arises in that the existing released Dropbox client for Linux is a module addition to Nautilus the graphical file manager. There is an API, unsure as to the stability of documentation on said API, that will allow open-source clients to be developed that can communicate with Dropbox accounts. At this time I am unaware of any that would work from a hosted shell account.
Updated to say I found this mention of experimental instructions for a text-based only install which may be usable for this situation but haven't tested myself.