Well, my neighbor has a small pond in his yard and he is continually restocking it with koi because they continually disappear.
Perhaps they’re all migrating to the ponds described in the OP.
Aided by our local raccoon population, of course.
And don’t forget about Chinese Snakeheads… I’m shocked no one mentioned Snakeheads yet!
And of course, the ultimate answer to the OP’s question is “It depends on how big a hole, and how long you wait.”
You know, the OP didn’t actually come right out and say anything about “spontaneous comefishin”. “Appear” simply means “show up”.
All you cynics are too ready to jump bad at the first chance you get. 
I have no trouble with the idea that those fish could somehow just show up. Either by birds, or simply falling from the sky. Which possibility has already been well cited. What if frogs bring them, huh? Or gators. Especially in locales where there are a lot of fish.
When I first saw the thread title, my first thought was “walking catfish”. My second thought was, it’s fairly common for people to release goldfish (among other critters) they have gotten tired of into a nearby river, stream, lake, whatever. I suppose that someone seeking to turn loose a coupla goldfish they don’t want to feed anymore might find a hole full of water an attractive place to put them.
Well, I dug a 1/2 acre pond on my property and within a year it was teeming with tadpoles and bugs!
Within another year there were minnows!
Minnows is fish!
Fact,Jack!
Bear poop, beaver poop, bird poop, etc. Anything that might eat a fish and poop in a lake.
My WAG is that it’s not unusual for a fish egg to survive passage through an animal’s digestive tract. We all know that corn kernels remain intact passing through us, why not a fish egg?
I was attempting to point out that IF alligators can arrive unseen, so can fish, the method of arriving notwithstanding. Even so, it is remarkable how far gators will travel to find water during the dry season.
Seemingly spontaneous fish appearances often occur when flying fish migrate for the seasons.
Sorry to burst some bubbles of skeptics… I have a pond, about 300 gallons or so. just a little thing for decoration. i had three gold fish which got eaten by a racoon or possum. 3 months and all i have done is clean the filter and lights. today I found about 10 fry of some sort. not guppies or gold fish as i know those. I have no idea where they came from. no one would “stock” my pond. most neighbors fear my dogs so not a pranker. you cant fish a bath tub. and i dont think coons or possum would stock it eother. “Spontaneous Generation” seems almost plausible. its a plastic pond so not “encapsulated” lung fish, they arent tad poles, and i rarely have birds in the pond as the dogs love raw sparrow. there is no reason for these fish to exist. i thought maybe suspended animation of eggs… but i only ever had 3 gold fish… try and explain it - i cant.
Funny…I see an awful lot of explanations (from 8 years ago, given, but…) up above. But obviously William of Occam could shave smooth as a baby’s bottom with a claim of spontaneous generation…
Why not? Both of those animals regularly forage near water and it would be easy to get some microscopic fish eggs stuck to their fur.
I used to water my zombiefish, but then I took a crossbow arrow to the eye.
Zombie fish could repopulate any body of water where fish once lived.
Also, possibly relevant, my father could toss a hook in a puddle of dog pee and pull out a fish. So there are great mysteries here.
ETA: Zombie ninja’d
Hey! Has anyone mentioned zombie fish?
Goldfish fry raised in a pond may not look the same as those raised in an aquarium - in colour especially - as this is partly dependent on diet and other local conditions.
Have you imported any plants - pondweed, marginals, etc?
I’m surprised this is such a mystery, I learned about this phenomenon in ecology class as an undergrad. It was apparently used as evidence for spontaneous generation, back when people still debated such things. The real culprits are birds and animals who unwittingly transport eggs or larval fish to virgin water bodies. I remember learning about an experiment in which two ponds were dug and allowed to fill in with rainwater. One was fenced in and covered with mesh netting that prevented birds from landing on the surface, the other was completely open. They tracked the ecological progression of both ponds over several years, and the fenced progressed more slowly than the open one.
Just realised - another potential vector for kanaka’s scenario - the dogs. Take the dogs out for a walk in the woods - fish eggs could be tracked back to the garden in mud on their paws, water in their fur, maybe even inside their mouths if they drank from a wild pond, then later, the one at home.
There are plenty of lakes in Norway where fish have not arrived after near 10 000 years. So “eventually” can, at least in some cases, be more than 10 000 years.
Usually water just sitting in a hole will stagnate and get stinky.
We had that happen at our lake property. We had the area by our boat dock dredged to make it deeper. A few years later the Corps did something with the dam and our section of the lake dried up for over a year. Except for that area we had dredged. That water stunk.
I don’t think fish can live long in stagnant water?
we dug holes (even little ones 1ft in dimeter or so) in the ground as children in the Caribbean just to see fish mysteriously appear after some time and in no form or fashion i am speaking about close to the beach, river or any other water source other than an open yard and rain