Dropbox-like client for Macs to access existing FTP/WebDAV/CMIS storage

We have many users on Macs that access their files on one big non-Mac server that supports FTP/WebDAV/CMIS.

PROBLEM: They can not use their files while not connected to the Internet.

QUESTION: Is there a Dropbox-like software for FTP? or WebDAV? or CMIS?

• When connected, pushes local changes to the server
• When connected, polls the server every n minutes to pull changes
• Preferably open source
• Dropbox-like UI: Tray icon, minimal configuration dialog, maybe green check in Finder to show which files are synchronized.
• Starts automatically at boot or login

Just to make it clear: I am not looking for an online hosting service. I have an existing server and there are no plan to move any data to any cloud. I am looking for a client-side software that can synchronize local files with the server when connected to the network.

• FTPbox is nearly perfect and open source, but it has not been ported to Mac yet.
• GoodSync does not work in the background (requires user click) so it is a no-go.

I was asked to add a short section describing why DropBox is not a solution: 1) Documents are confidential, third-party is not an option 2) Dropbox is not reliable enough (better uptime/SLA is needed) 3) Dropbox becomes crazily expensive for large scale 4) The FTP/WebDAV/CMIS interface is actually provided by "Alfresco", an enterprise document management system which has many other features (not just file transfer), and is integrated with other critical enterprise systems. So my question is really about client-side only.

You may want to look into the following open source applications:

• FTPSync

  a Perl script to synchronize a local directory tree and a remote FTP directory tree.

• ownCloud

  Web services under your control.

  Current features: file management, WebDAV access, share via public link, music streaming, users & groups, OpenID, LDAP In development: sharing, encryption, calendar, contacts, etc., desktop sync client, Android & webOS apps, server-server sync

  NOTE: You do not have to utilize their storage.

CmisSync is just like Dropbox, and syncs with any CMIS-compatible server:
SharePoint, Documentum, FileNet, Alfresco, Nuxeo, DocuShare, Oracle, Lotus, SAP, Windchill, etc.

• Syncs both up and down
• File stay accessible when offline
• Conflicts are handled like in Dropbox

Open Source.
Disclaimer: I wrote CmisSync as a fork of SparkleShare, the tool mentioned in Patrick's answer which unfortunately supports only the Git protocol.

You can try IQ Uploader.com. For disclosure, I am the main developer working on this project.
It does exactly what you describe, and provides FTP sync for MacOs and Windows. It also uses FTP-SSL/TLS by default. It syncs local changes in real-time.
We just released a very usable Mac alpha that you can download. The official Mac beta will be released by the end of 2014.

I had a similar requirement when trying to work with files on a remote FTP-Server from several clients. For me the best working solution on OS 10.11.4 is Fuse for OS X together with MacFusion.

The first one can be found on sourceforge:

https://sourceforge.net/projects/osxfuse/files/

Fuse is the "background-package" which basically extends OS X-file-system-capabilities. (Some older tutorials point to MacFuse, which is, from my understanding, an older version that is not supported anymore.)

MacFusion is kind of an UI for Fuse. Basically, you don't need to know more than your credentials to access your FTP-Server. Here I found a (quite old) tutorial with screenshots from an older MacFusion-Version, that still works, anyways:

http://www.simplehelp.net/2008/07/25/how-to-mount-a-remote-file-system-as-a-local-drive-in-os-x/

hth