How common are eye parasites and is there a risk of infection from standing water?

It's unlikely you'll get a parasite from puddles even if they are present. However, it's always important to use a reasonable measure of caution if you suspect the presence of parasites in standing water.

Parasites are organisms that live off their host (humans in this case). Parasitic infections involving the eye can range from rare and potentially vision-threatening (such as Acanthamoeba, Toxoplasma, Toxocara, or Onchocerca) to very common and much less serious, such as Demodex, which are very tiny mites found in eyelashes and other parts of the face.

Each parasite has its own way of entering the eye (for example by bathing in or swallowing contaminated water, insect bites, swimming with contact lenses), so one should take safety measures and practice good eye hygiene to prevent infections from parasites. Some of these include considering insect repellant in areas at high risk, avoiding eating raw meat, hand washing, avoiding touching the eyes unnecessarily, and properly handling contact lenses. If you have any symptoms that you are concerned about, you should bring them up with your eye doctor.