What I do care about is being met with something cutesy in the face of a technical failure anywhere on the net.
I hate Amazon's failure pets, I hate google's failure mini-games -- it strikes me as an organizational effort to get really good at failing rather than spending that same effort to avoid failures all together.
It's like everyone collectively thought the standard old Apache 404 not found page was too feature-rich and that customers couldn't handle a 3 digit error, so instead we now get a "Whoops! There appears to be an error! :) :eggplant: :heart: :heart: <pet image.png>" and no one knows what the hell is going on even though the user just misplaced a number in the URL.