As far as I am aware there is no free service that you ask for. Simply ask yourself the question of why would anyone pay to let you use something they can charge for. Certainly not 10gig sized one anyway. You could consider buying a pocked hard drive as 20gb 1.8inch drive ones are quite cheap these days. You can also build your own if you wish to save money. Personally I went out and purchased a 40gb hdd player and enjoy it anywhere I want and take 1gb SD card with a nice chunk of my music to use on my treo phone.
The only alternative is to buy or rent a server but again that isnt free however if you know the right people they may be able to run it for you provided you offer them to use the rest of the space on the machine.