Fun with copyright violations!
Beholder -- Big Eye -- Dark Eye -- Death Beholder -- Death Eye -- Deep Eye -- Evil Eye -- Eye Fang -- Float Eyeball
Beholders are creatures from Dungeons and Dragons. They're basically flying balls with mouths and eyes - one large one in the middle of the face, and a number of smaller ones on stalks. Beholders are, according to the D&D, "the stuff of nightmares". Some beholders are undead - these ones probably inspired the death beholder.
IMAGE: D&D's beholders. The one in the bottom right is undead.
The big eye was probably created by Square - it's definitely not the first creature to be comprised of a pair of eyes (during Wold War II, airmen lodging in an Italian castle reported seeing two eyes peering out of the darkness), but since it obviously didn't take a good deal of imagination to come up with the design, I don't think I really need to go looking for an inspiration. The eye fang is more unusual, however - it seems to be partly modelled around the Venus' flytrap or an blossoming bud with teeth.
IMAGE: D&D's beholders. The third one from left is an eye of the deep.
Square got in trouble with TSR for including beholders, copyrighted D&D characters, and so replaced the beholder and death beholder with the evil eye and death eye in later versions of Final Fantasy. Strangely, the other enemies that Square lifted directly from D&D were allowed to remain.
IMAGE: D&D's beholders.BEHOLDER, DEATH BEHOLDER

BIG EYE, DEEP EYE, EYE FANG, FLOAT EYEBALL

The deep eye could be inspired by D&D's eyes of the deep, a type of beholder. The float eyeball is modelled around FF3's Ahriman.EVIL EYE, DEATH EYE

These two monsters are pretty much just generic beholder lookalikes. The evil eye's name is taaken from a piece of widespread folklore - in a number of places over the world, witches are said to be able to place a curse on someone by looking at them. This curse is known as the "evil eye".