One buyer wanted to keep the sellers dog as part of the sell.  The seller agreed.  I could never give up my dogs.

I had a client ask if their pooch could ride with us.

I once had a proposal.  I turned it down, he still bought a house though. 

My client wanted me to date him. He was rather smitten shall we say. He even tried to sneak kiss me once.  Weird. Inappropriate. Uncomfortable.

I didn't find this one too strange, but it was a first:

Clients said they did not want to buy a property that 4's in the address.  I spent a lot of time sorting properties manually so I could exclude anything with a 4.  

The clients were looking online all the time asking why I didn't send them this property or that one.  Of course, they all had a 4 in the address.

They bought a property whose address was 2944.  

They divorced a year later.  I don't know if it had anything to do with the 4's.