I've used IA to research things I would not have been able to any other way, the information is _no where_ else!
* Finding missing YouTube videos from playlists. It's usually enough to get the title as YouTube doesnt care to show you the title of what's been deleted, privated, etc.
* A large university deleted all their "website builder" pages including a lot of research and news about certain projects. I used IA to find information on a building I bought from them.
* Looking at the origins/roots of companies like Unity3D. Have you seen their website in 1999? It's pretty cool!
* Old tutorials on websites that don't exist anymore.
There is so much use to IA when those that store our information would gladly pull it out from under us to save a few dollars.