You can't really put huge amounts of data on a Blockchain. That being said, I've wanted to start a distributed YouTube project, where every video you watch gets downloaded/cached and then reserved up. People running a browser plugin could stream movies off each other rather than from Google.
This would keep movies alive after take-down requests, but you'd need to ensure the video wasn't poisoned (someone broadcasting they have a video when it's actually something entirely different). You would need to hash the video and store the hash on the blockchain. If Youtube changes the video (removes audio) you'd need to keep multiple versions of that video on the chain and clients would vote to confirm that those hashes were legit for when that version was up.
You'd also want to have some system to let you know if videos you have are no longer on YouTube (incase you want to delete them or if they have illegal content) and videos could still disappear, but only after everyone who has a copy decides to stop hosting them.
It would totally violate YouTube's TOS, but it would be the start to a more robust, distributed and democratic video hosting ecosystem.