I'm an optometrist in the U.S. and have a couple of memorable ones.
I had an argument with one patient who insisted that there were great healing benefits to using urine eye drops. When asked about how she got these urine eye drops, she admitted to taking them directly from the toilet and putting them straight into her eyes. My pleas for her to consider the risk of developing bacterial keratitis fell on deaf ears. Still dreading the day that one returns to clinic with an infection.
And if I had a nickel for every time a patient came to me ~6 months after taking a severe blow to the eye and losing vision, only to find that they had a total retinal detachment that they thought they could just "walk off" instead of seeking care, I would have two nickels, which isn't a lot, but it's weird that it happened twice in the three years I've been practicing.