One thing I have done is to upload the Family Tree to the World Family Tree, a commercial database owned by Broderbund Software, makers of the Family Tree Maker software. I know there are other sites and organizations that will archive information, and I'm working on that.
However, there is more to the family history than the bare electronic data. There are photo albums, documents, stories about our ancestors . . . perishable material, all, that may survive, or may be lost. I've watched people throw away such things, when there was no one left alive to tell them who the people in the photos were.
It may be possible to set up some kind of endowment or trust for such things, even if it's only a dry storage spot somewhere. It might also be possible to keep a website like this going in perpetuity, for future Lugtharts. The present cost is about $350.00 a year for the domain name (lugthart.org) and 10 megs of storage on the ISP server. If there's one volunteer out there in each generation, it might be possible to keep it going. But that's just a fantasy, at present. If you have any ideas or espertise about such things, get in touch. Maybe it doesn't have to remain a fantasy.