I've been using BitTorrent Sync and I'm really happy with that. I can sync whatever I want including big files and I don't need to worry about running out of space as long as there's still disk space on my server. I think that's better than Dropbox, since Dropbox only gives you 2GB by default. Plus, the data is kept in other people's computer and I will never know what they will do with those data.
However, BitTorrent Sync lacks one important feature. You can't share your files with others by giving them URL links. They need to have BitTorrent Sync installed also. So, how are we going to solve the problem here? It's actually pretty easy. Just let the web server serve the files you want to share. Basically, create a directory that can be served by the web server. Then let BitTorrent Sync watch that directory.
I did that and it has been working well so far. When I need to share my files with others, I just put the files into the directory. Then BitTorrent Sync will start downloading the files into the web server. All I need to do here is make sure the files are there and then give them the URL.