Got a few...
Years ago, when I worked as a shelf-stocker in a grocery store, a woman walked up and started asking me about head lice. I guess because I was roughly near the pharmacy I looked like I must be an expert; must've spent five to ten minutes as she asked me about head lice, worried whether she had head lice, and wondered what to do about head lice if she had it. I finally managed to steer her to the pharmacist. (Never did find out if she actually had head lice or not, though... one of those subplots in my life that will never be resolved.)
A while back, our family was in a park near a large bronze statue depicting a logger and his ox team, larger than life. While we're standing there, a guy walks up and starts complaining about how they always make statues of bulls instead of steers - you can't work with bulls, damn it, but everyone wants bulls! The guy's father, evidently, had been a woodcarver, and customers always insisted on anatomically correct male animals, even when said anatomy would invalidate the authenticity - as in the bull/steer conundrum. We must have somehow looked interested, because he kept going on and on and on about it. Standing in a park on a sunny day, listening to a man rage about bronze bull testicles... ah, memories...
And then there was the slow day at my current job, working the Saturday shift. The Saturday shift's always been a little... odd. Anyway, I overheard one of the older ladies talking about self-defense and firearms. She declared that, if she ever shot an intruder, she'd want them to suffer before they died - none of this "drop them in one shot" bull. Make 'em bleed, put the fear of God into them. After all, they broke into your place, not the other way around. (There's a reason I don't work the Saturday shift unless I really, really need the hours...)
I know there are more, but those are the ones that linger.