A couple of my favorites.
Where do you end up if you dig a hole straight through the earth?
Where I grew up, Los Angeles, we all knew that the answer was China, though apparently the correct answer (for 80% of the world, Los Angeles included) is drowning in one of the oceans. I've asked many people this question, and almost all of them, even though they've grown up in a wide assortment of places, think that China is the answer. I've never asked someone from China.
Does water swirling into a drain in the southern hemisphere swirl in the opposite direction from water swirling into a drain in the northern hemisphere?
For many years I knew that the answer was yes, and wanted to travel to the southern hemisphere mostly for two reasons: to see the stars and to watch the water go down the drain in the opposite direction. A number of years ago, however, I learned that I could still use the stars as a reason for making the trip. It turns out that the Coreolis effect is very real, but insignificant on the level of water in a drain. It's a disappointment, but I've learned to accept the truth.
Any readers who want to add to this list of questions are invited to send their queries to me. I'll be happy to add them here.