At my university, the radio station held a massive all-day quiz competition. Google was still relatively new, but they adapted by making the questions more compound and reliant on some familiarity in a domain (e.g. What would the mass of the world's heaviest man be in picograms when using the IPK as measured in 1889?).
There was also a scavenger hunt component to the contest. One such item was a photo of a famous annual naked soccer game that you couldn't have had unless you were actually there in previous years. This was before Google Images (I think), so I had my friends go outside in their underwear and then Photoshopped them onto a picture of a soccer field.
Edit: in response to what you said about the dangers of over-relying on Google, I remember there was a quiz question that required knowing some fact that could only be found in some obscure printed book (again, probably before Google Books was around). So I altered a Wikipedia page (each quiz question allowed for several minutes until calling an answer in) to mention a fact that coincidentally matched the answer we called in, and when the radio station said we were wrong, we successfully disputed their answer by sending them a link to the Wikipedia page.
I think the page was reverted back soon after, because other teams were doing the same thing from the university IP and there was a temporary blanket hold on edits from our IP when Wikipedia editors noticed what was going on.
There was also a scavenger hunt component to the contest. One such item was a photo of a famous annual naked soccer game that you couldn't have had unless you were actually there in previous years. This was before Google Images (I think), so I had my friends go outside in their underwear and then Photoshopped them onto a picture of a soccer field.
Edit: in response to what you said about the dangers of over-relying on Google, I remember there was a quiz question that required knowing some fact that could only be found in some obscure printed book (again, probably before Google Books was around). So I altered a Wikipedia page (each quiz question allowed for several minutes until calling an answer in) to mention a fact that coincidentally matched the answer we called in, and when the radio station said we were wrong, we successfully disputed their answer by sending them a link to the Wikipedia page.