Yacy is an open source distributed search engine. Basically, you can have it crawl whichever websites you want, or you can even send it up as a transparent proxy so that it knows which websites you've gone to and it will crawl any websites you've ever been to, and it hooks up with everyone else running the software so when you run a search, you end up searching all of the things in your index, as well as all the things that everyone elses index. Kind of like bittorrent, it also has each node on the system pass around different chunks of data to each other, so there's lots of different copies of different pieces of the index everywhere.

I've got a copy set up at https://yacy.fbxl.net

You don't even necessarily have to use it exclusively, because it can hook into a searx instance so yacy results are just one piece of the total results. That's how I've got my search.fbxl.net set up, it looks at a bunch of different websites, and yacy is just one of them.