Are there any monocular animals? There must be...

I had a dream. A nightmare, actually, which starred me being chased by a Spielberg velociraptor animal except for instead of a neck and reptilian head it had, in correct sizing of that combined length and neck width, a bellows-like short elephant-trunk-y appendage ending with an eyeball peering out, half embedded like in our eye socket.

So.

See subject.

Many birds have eyes almost on opposite sides of their heads, such that the stereoscopic portion of their field of view is extremely narrow.

Bilateral symmetry is so common in animals, down to the smallest, that I can’t think where a single-eye physical form would come from.

Low on the bio-complexity level but howsabout the euglena?

The starfish has a single eyespot.

There’s a type of tiny crustacean called the Cyclops or water flea.

There is a species of jellyfish with a single eye. The eye is badly farsighted. I can’t remember the name of the species. I learned about it here on the Dope.

Starfish actually have an eye at the end of each arm, so most species have five of them.

There are spiders with an uneven number of eyes. One of those must fit your criterion.

What would the evolutionary advantage be?

I don’t think so. Every close up of a spider I’ve ever seen shows at least two eyes.

Re Jellyfish

Some quick Googling has turned up that all jellyfish eyes are farsighted. I can’t find a page with a pic of the one eyed jellyfish yet.

I’m wrong. But there is the tuatara (q.v.) that has some sort of third eye that scientists haven’t quite figured out.

More to the point, Triops is a shrimp with a third eye in the back, which appears to be capable of sight. From behind, Triops is effectively a one-eyed creature

The tuatara probably can’t see out of that rear eye, which seems to be associated with daily rhythm. The human pineal gland is similarly light-sensitive, despite being inside the brain and away from light.

Opabinia had 5 eyes on short stalks, one of which was unpaired.

It also has a trunk (proboscis) with a grabby mouth-like thing at the end.

I’ll bet it somehow invaded your dreamscape and somehow mated with a velociraptor.

Probably none. That’s why if there are any, they’re rare. But perhaps their one eye is somehow linked to a characteristic that is an evolutionary advantage.

Lots of insects have a cluster of three ocelli on their foreheads. Hymenoptera (bees, wasps, and ants) and cicadas spring to mind, but mantids have them too. Looking for pictures tells me that plenty of others have them too but you never see them because they don’t let you get close, like mayflies and dragonflies (squashed in between the compound eyes) and damselflies and even flies. That last one surprised me because I figured the more “advanced” insects had all lost them, since beetles and butterflies don’t seem to have them.

Those are all multiple eyes though, even if they are odd-numbered. Like Prof. Pepperwinkle, only living thing with no more than one eye that comes to mind off-hand is Cyclops. If extinct critters count, back in the day there were monocular trilobites, I think I saw a fossil of one at the Smithsonian but it’s hard to find good pictures of them online.

Cite?

According to this Wikipedia article, the box jellyfish is the only type of jellyfish that has eyes that focus light at all. Others only have simple eye spots or pits, that do not form images, so the concepts of near or far sighted is not applicable to them.

Furthermore, I have difficulty believing that box jellyfish have gone to all the trouble of inventing eyes that can focus light, only to leave them all with sub-optimal focus. They may (very likely) not be able to change the focus of their eyes, like humans can, and it may be that the focus is fixed optimally for distance rather than close up, detail, vision, but that is hardly the same thing as “farsighted” as that term is applied to humans.

Quick googling at work failed to turn up a picture of the famous “One-Eyed Penisaurus” from Flesh Gordon. Nor did I want to look too hard while at the office!

Get ahold of Retief, the Groaci are invading.

Many vertebrates from fish to reptiles have some version of this third or parietal eye. The tuatara has the best developed version among living forms. However, many extinct species may have had more functional third eyes in between the two lateral eyes.