If I was a web search company, I'd allow users to upvote or downvote their search results (this would increase or decrease their prominence on subsequent searches). This could be done on a per-site, or per-page basis.
Then I'd use one person's preferences to alter how other people receive search results (on an optional basis; if people didn't want their results filtered like this, they wouldn't have to.)
But I wouldn't just use an average of all users; it'd be too easy for spammers to create fake accounts to upvote spam. No, a user's search results would only be affected by what their friends upvote and downvote (or possibly their friends of friends as well).
This would make it in a user's interests to link to their friends and have their friends rate websites, as everyone uses web search. So people would want to promote the search engine to their friends.
To give people more of an incentive to proselytise the search engine, I'd add social features such as a twitter-like service (allowing public, friends-only, and named-recipients-only messages), chat (text, voice and video-voice), an extended-length messaging service (you could call it, I don't know, a "blog" or something) that also allows pictures, and RSS feeds of one's own and one's friends' public entries.
I'd also add a "fan" feature (intransitive, as opposed to friendship which is transitive). People could create lists rating websites, and others could fan those lists.
Maybe someone like DuckDuckGo might want to implement something like this?
(Incidentally, DDG market themselves as being privacy-friendly, which coupled with the recent subpoena of Wikileaks' Twitter data, suggests there may be an opportunity for a competitor to Twitter that is more privacy-minded).