I have a few favorites (both from Davis, CA).
There was this guy from Berkeley that came up to Davis and I was working the counter that day. He wanted to ask some questions about the time door. I was thinking, "okay... maybe he means timer locks on doors", and I went and got a building code officer. Nope, he meant the TIME DOOR that his buddy told him was in Davis. He said he wanted to go back in time to get his kids before the divorce. Poor dude, totally lost it. I got crap for months after that from the building code guy though...
Another good one is a guy that wanted to know about zoning and use restrictions if he wanted to build a city under the rest of the city. I said that there weren't specific regulations, but there would be problems with utilities, so I sent the whack job down to public works to bug an engineering friend of mine. She was annoyed, but then had a good laugh over it.
We had lots of others, like a guy that built an A-frame shed so he wouldn't be stuck with the height regulations, since height was measured at the average between eave and peak. I wish I could remember all the weird questions and stories. There were lots of good ones.