Archive.org is an important non-profit US based organization and they are doing an incredible job at archiving the web. But, they are not perfect and they can not be the only ones.
Goal: there should be a P2P alternative to web archiving.
So as a start, here are some ideas to get started on a personal archive.
By using Wallabag or Respawn (or something similar), it is possible to keep a copy of a web page. These systems could then be fed with RSS feeds coming from a Shaarli instance or any other list of bookmarks.
A search engine like Yacy, can be used to index the save pages.
This doesn't create a multi-user distributed archive, but it's a start.