BitTorrent presents a plausible (but not complete) replacement. Most torrents nowadays are disseminated through the DHT. User clients can query the DHT to search for specific content, which is then downloaded via its content hash through trackers. Many websites are also available which provide indexes and other features (comments, virus scans, ratings, etc.) on top of this DHT database.

It would be a technical stretch to expand this to replace Google, but if you did you'd have many competing "search engines" built upon an open decentralized database.

I don't think I've expressed this idea well, but you should get the gist.