This was a fun compilation on the most common Google search questions by state, 2004-2016. The results are not the most common questions asked, but rather the questions asked more commonly in that state than in any other state.
More on this compilation and a full list of the questions by state:
Estately Blog
My favorites from the list (that are not on the above map):
Arkansas: Why did the chicken cross the road?
California: What is a mullet? Where is the nearest Starbucks? Do jellyfish have brains?
Florida: Which Disney princess am I?
Georgia: Who created God?
Indiana: How many states are there? What is the constitution? (both these ?!!) Do midgets have night vision?
Iowa: Do penguins have knees?
Massachusetts: Who’s on first? Where have all the cowboys gone?
Michigan: Where is Canada? (isn't it next door?)
Mississippi: Who am I? Are mermaids real?
Missouri: Am I a psycho?
New York: Where my dogs at?
Pennsylvania: Why can’t I poop? Do cats fart?
Texas: Am I a sociopath? How does sex work? Do girls poop?
Vermont: Where is my mind?
West Virginia: Why are cats afraid of cucumbers?