What is the most successful animal species that doesn’t possess eyes?
I suppose folks will quibble over the definition of “successful” and “eyes”. Define success by your own criteria. Eyes are sensory organs that perceive objects. So I would say compound eyes and eye cups and spider’s eyes are eyes. A light-sensitive cell is not an eye because it doesn’t know what direction the light comes from.
I guess ‘worm’ may be too simple for my point. I didn’t consider termites, which are pretty successful considering the ecology for all land animals would be quite different without them or some other animal in their role. Mussel varieties are found all over the place in both fresh and salt water, though they must be pretty diverse species. But I can’t think of a reptile, bird, or mammal that could be called successful without eyes. I can’t even think of a bird without eyes at all. I’ll bet Colibri would know if there was one.
I’m going with some kind of sedentary aquatic life form - coral, probably, but sponges, anemones, tube worms, etc. should also be in the running.
I know that the bulk of material in a coral reef is technically dead, but there’s a lot of living material on the surface, and coral survives across a large portion of the world’s surface and has done so for long period of time.
Maybe something planktonic? Hell of a lot of microscopic animal biomass there. Though after [del]browsing wiki for five minutes[/del] extensive research, it appears that most of those arthropods have eyes. Rotifers, too, have extremely simple eyes, though most of those are closer to light detecting cells. Hydra don’t have eyes, though other cnidarians do have “eye spots” which probably don’t meet the OP’s criteria for an eye.
That is not really true. Animals with eyes consisting of a single light sensitive cell, do indeed use them to sense the direction of light, and guide themselves towards it. Indeed, I don’t think the cells are used for much, if anything, else. In terms of the numbers of such organisms, they are very successful too.
As for the actual answer to your question, no idea.
They have made their niche living in muddy rivers, and their eyes have devolved into little more than vestigial remnants. They lack a crystalline lens, and are commonly described as being blind – although it’s not entirely clear if they are totally blind, or if they can see vague unfocused light.
Technically, there aren’t any single celled organisms in the Kingdom Animalia under modern classifications. The Protozoa (single celled Eucaryotes) are generally classified as the Kingdom Protista (or according to some Protoctista) these days. (However, according to a cladistic classification, the Protozoa themselves are polyphyletic and would contain a dozen or more clades equivalent to Kingdom rank.)
Within the Animalia, I would probably go with nematodes as a group. They are extremely abundant, and they are almost everywhere. I’ve heard it said that if everything but nematodes disappeared, you would still see the ghostly shapes of the soil, trees, animals, plants, and people outlined in the nematodes they contained.