Consolidating suggestions here:
1. http://www.tonido.com/
2. http://owncloud.org/
3. https://www.aerofs.com/
4. http://www.bitcasa.com/
5. https://spideroak.com/
6. http://www.sparkleshare.org
Also, you can backup/sync/share arbitrary folders.
Alternatively, use a git provider such as github as a backend - I'm not sure "secure" is the right description, though, if you do that.
1. Tonido is out of the game, because the file syncing is limited (2 GB) so it is useless for me.
2. OwnCloud looks very good. I am going to try it..
3. AeroFS - In theory what I need (but unlike onwcloud is not open source) but in reality the experience was terrible - sometimes it didnt sync my files for no apparent reason, sometimes it eats too much memory.. I didnt like the experience very much..
4. Bitcasa seems too magical, I dont know how it works, I dont trust it..
5. Spideroak looks just like another dropbox, dont need that..
6. Sparkleshare is good idea, but using GIT as syncing mechanism means that it is not suitable for media files, so it is out of game for me..
So my hopes are with OwnCloud :)
I have been using mediacloud ( http://mediacloud.cc/ ) for the past few months and I've been very impressed with it. They have built-in file acceleration to give you the maximum upload speeds your network allows. I've been using it to upload files anywhere from 1mb to 20gb and have never had a problem.
As for security I know they use AES256 SSL, but again, am not sure which aspect of security you are interested in.