You can search through indexes that do not live on one server (are decentralized). This is required on IPFS, because there is no one server. The searching and sorting is happening in your browser.
The reference index (maintained by me) is Wikipedia article abstracts:
If you want to create your own index, the instructions on how to do it are here.
One public index I've come across is the The Pirate Bay Dump, you can find it here:
/ipns/QmWK2jjuFaHds5CEA9AQsGjGUmAyxUMXdzdiz2cK8TokL4. Note that I have no control over the index. The author writes more about it on reddit.
Since there is no one server, there is also no one server that could be taken down. It is impossible to take down an index after it is uploaded to IPFS.
Traditionally, when you search for something on the web, you send your query to a server. The server then (basically) takes your query, looks up the relevant documents in its index, ranks the results and sends the results back to you. This is how search works on Wikipedia, DuckDuckGo or Google.
With IPFS, it is impossible to send your query to a server, because there is no single server. With ipfsearch, your browser first downloads a document that tells it, where it can find what part of the index. Then, it downloads the required parts of the index from IPFS and does the lookup and ranking itself.
Most of the delay is caused by IPFSs DHT being slow. The performance of ipfsearch is expected to rapidly improve once the IPFS DHT gets faster.
The newest usable version is always at ipfsearch.xyz, or
/ipns/ipfsearch.xyz. In case the domain doesn't work, use
Download IPFS from the official website, start the daemon on your computer and dial http://localhost:8080/ipns/ipfsearch.xyz in a browser.
You can find the source code of this at Github. Issues and PRs are welcome there.
The web part of ipfsearch is licensed under the GNU Affero GPL 3.