Strongsync is a personal Dropbox style syncing service that lets you use your own FTP space or Amazon S3 storage instead of Dropbox's servers. It creates a "Strongsync" folder in your home directory and anything you drag in there will be synced across to your other computers that are set up with the app running.
I've tried it with some FTP space that came with a domain name and also my free Amazon S3 account. Although it worked with both, I got a monthly bill ($1.55) from Amazon for overuse charges. There were over 250,000 file requests, and since I haven't used my Amazon S3 for anything else during that period, it would appear to be Strongsync that has pushed me over the free usage limit. I've now switched back to FTP.
Strongsync doesn't so everything that Dropbox does. There doesn't seem to be any way to sync data to a mobile device. There's no iOS app. No public sharing of files. There's no easy way to access the stored data directly from FTP, since the file names are garbled, and there doesn't seem to be any archiving of deleted files. It also seems to work a bit slower for me than Dropbox, but that probably depends on the speed of your FTP servers and connection.
It does the basic syncing OK, though, and if you need to sync more than your Dropbox account can hold, and if you have enough FTP space, it's an alternative worth considering.