Just like how songs, writings, films and pictures are still found today even when it was made 200 years ago. Will the same thing happen with youtube videos 200 years from now even when youtube is done? It's a question i always wondered.
To be honest, Youtube will never die. Every other video sharing site (dailymotion, vimeo, etc) is so far behind that nothing will be able to topple them. Especially with Google owning Youtube, I don't think it will be going away until hell freezes over.