Honestly I don't even want to think about it.
I've become quite reliant on Youtube to cure boredom.
Then again, if its just Youtube then... well... there are the other video streaming sites so.
Initially it would suck.
But I think it would spark many youtubers to actually make a website of their own.
The popular youtubers would have viewers coming specifically to their page to watch their content and only get sidetracked in their videos.
My point is, It'd suck, but I would eventually move on probably if it were to shutdown permanently.
If were' talking temporary then... well, I'd suck it up and try and occupy my time however I can.