Check out Pertino.com, a network as a service startup. You can set up a free account for three devices forever. If you need to expand past three devices at the same time, then Pertino has become valuable to you.
At a minimum, you get a very easy to use (and administer) private, secure network between you and whomever you invite onto your network, so you can do Remote Desktop, VNC, X, or whatever else you choose for you and your family to use without resorting to GotoMyPC, WebEx, etc. (mind you, all of those solutions are valid Desktop Sharing services, too) . But you can also do NFS, SMB, FTP, etc. for file sharing. Or anything: you finally have a virtual private network where you and your remote clients/family get a LAN-like experience in the cloud.
Full disclosure: I work there, so I am hopelessly biased. The value I see in this solution is that it is easy and secure for everyone, covers mobile and desktop, and allows you to try almost any solution out there to solve your needs because you have a peer to peer network with remote devices.