The ghosts of the ancient Romans are referred to as shades of the dead, who were honored or propitiated by means of festivals throughout the year. This isn't very different from our honoring the dead in the festival period from Halloween through the Day of the Dead.
There were several types of Roman ghosts, particularly Manes (Di manes), Lares, and Lemures. The ghosts were also known as umbrae (which translates as 'shades', as in "umbrella"), imagines, and species. The behavior of the shades varied, but there isn't a real consensus among the ancient sources on which shade did what.
The Manes were generally considered benevolent. Some of the ghosts harassed the souls of the dead in the Underworld, according to the Apocolycyntosis of Seneca and the Natural History of Pliny. These may have been the souls of those who died prematurely or violently, or both.
There were official days for propitiating the shades of the dead -- with beans. One of the holidays for the shades was the Lemuria, which Ovid said came from Remuria, a festival instituted by Romulus to appease the shade of his murdered brother Remus. Another festival for the dead was the Parentalia, described by Ovid in the Fasti (2.533), which was for the ancestral Di manes. The festival for the Lemures was the Lemuria.
The shades were physically described as immanes suggesting immensity and shapelessness, much like our representation of ghosts as swirling transparency.
Main Source: "Lemures and Larvae," by George Thaniel, The American Journal of Philology, Vol. 94. No. 2 (Summer 1973), pp. 182-187.