In the book The Lord of the Rings, the Eye of Sauron is within the Dark Tower, Barad-dûr. It is described as having flames on its rim. Sauron's Orcs use the sign of the Eye when they roam the Earth.
In Peter Jackson's movies, The Lord of the Rings: The Fellowship of the Ring, The Lord of the Rings: The Two Towers, and The Lord of the Rings: The Return of the King, Jackson envisions Sauron as being a spirit-like being who cannot (yet) take bodily form. Sauron's only physical presence is as a giant disembodied red eye, seen in the second and third movies as floating above Barad-dûr (or perhaps suspended by its twin parapets). The Eye is "constantly moving", seeking out all that moves in Sauron's domain of Mordor. In both the book and the movie, the effect of the Eye in Mordor is seen as a red beam that moves across the land, forever probing. The Eye is referred to as having the capability to "see all", although that must be meant as a term of fear and not literally; Sauron is not aware of most events that occur in Middle-earth.
Pippin had a brief and frightening encounter with the Eye, after gazing into the palantír of Orthanc.