After the Fall of Numenor, Sauron could never again take on a pleasing shape that would deceive anybody, in fact I think he may have been stuck in the form of a "Dark Lord" just as Morgoth was after the Darkening of Valinor.
In the battle at the end of the Second Age, Isildur cut the ring off of his hand, probably along with a finger, which shows that at the battle he was in a humanoid form. During the Third Age, Gollum described him as having hands.
The "lidless eye" in my opinion is not a physical form that he takes, it is a physical description of the telepathic experience of having him assault your mind through a palantir. Either that, or it's a description of what his eyes look like. Did anyone ever describe the lidless eye as disembodied, or give any other reason to assume it wasn't attached to a face? If the eye was extremely mesmerizing, or just compelled one to look at it, Frodo might not notice the rest of his face. Even dragons can do that.
Physically taking the form of a giant floating eyeball... what would be the use of this? He used his mind and power to search for the ring because it was a part of him, he didn't need to turn into an eyeball to do it, plus with his mind he could "see" in many directions at once, over the horizon, past obstructions, etc. He could use his mind to dominate his slaves, too. As a giant eyeball he'd have no hands, and he wouldn't fit in most rooms. He could probably get around the lack of a mouth using telepathy, but still. I just can't see it.
Edited by Aldandil, 30 June 2009 - 12:20 AM.