I know that Sauron has been disembodied once or twice in his day (after the downfall of Numenor; after Isildur cut the ring from his finger), but I had always assumed that, by the time he takes possession of Barad Dur again in Frodo’s day, he’s got his body back.
Lately though, I seem to be reading more and more that people think he has no body during the events of LotR. --Exacerbated, I think, by Peter Jackson’s focus on the Eye of Sauron … people seem to think he’s just a big, fiery eye. Me, I always assumed he had a body (doesn’t Gollum, in reference to his torment at Sauron’s hands, mention something like, “there are only four fingers on the black hand … but they are enough”?) but that his piercing lidless Eye was just a notable feature, and one that a ringbearer, fearing exposure and discovery, would be aware of.
So… body or no body?