I have a shocking number of these stories. I'm a very friendly-looking, non-threatening person so I guess people just feel comfortable talking to me about any old thing.
One time I was walking round town and made eye contact/smiled at a woman walking the other way to me (small village habits-hard to break) and she suddenly started talking about the weather to me, so I awkwardly stopped and made some non-comittal response. She mentioned she'd sat on a bench after it had rained and motioned to her arse and asked me if I thought she'd get a cold.
I was like "I don't think it works that way..." and then she asked me to TOUCH HER ARSE to confirm it wasn't wet. For some reason my response wasn't "Umm, wtf, no I'm not touching you..." but just repeatedly confirming that it didn't look that wet and I was sure she'd be fine because she wouldn't stop asking.
Eventually I managed to get out of that situation without fondling a complete stranger, but I will forever remember that day.