Do you know any software like Dropbox but using my own hosting space?

Here is a great tutorial on how to make your own Dropbox-like service! Be warned, though, it's a little involved. http://fak3r.com/geek/howto-build-your-own-open-source-dropbox-clone/

You have a few options.

Firstly, Dropbox now supports local LAN syncing, so you don't need to use the cloud. You didn't state if local is what you needed, but there's that.

Tonido is another great option.
http://www.tonido.com/

Then there's the homebrew mothod. Scenic, but it works and I know plenty who use this:
http://fak3r.com/geek/howto-build-your-own-open-source-dropbox-clone/

One can use there FTP or a WebDAV (Mounting as a network drive) to use there own hosting space. If you do not have those, One must upgrade to a webhosting plan that allows this. carefull not to use too much space.