In The Books
When the Nine Nazgûl were thwarted at the Ford of Bruinen near Rivendell, they were riding coal-black horses. Those steeds were destroyed in the flood caused by Elrond's intercession that vanquished the Nazgûl as they pursued Frodo.
After The Fellowship of the Ring had left Lothlórien and were camped on the western shore of the River Anduin, they saw a great winged creature, blacker than the pits in the night. When Legolas raised the great bow of Lórien and shot it with an arrow, it gave a harsh croaking scream and vanished into the gloom of the Eastern shore.
Frodo, Sam, and Gollum encountered a fell beast while passing through the Dead Marshes, wherein Gollum referred to the beasts as "wraiths on wings".
According to the chieftain of Harrowdale, a fell beast flew over Edoras and stooped just over the great hall of Meduseld. They described it as being darkness in the shape of a monstrous bird. After this, Gandalf told the Rohirrim to assemble at Dunharrow rather than at the fields to prevent attack.
When Faramir, captain of Gondor, was fleeing from the besieged city of Osgiliath on his way to Minas Tirith, he was many times beset by winged Nazgûl until Gandalf rode out and drove them away with a shaft of white light from his raised hand, most probably from Narya, the invisible ring of fire, of which he was the bearer.
During the Battle of the Pelennor Fields, the Witch-king of Angmar arrived in battle mounted on a fell beast. When the Witch-king successfully and fatally injured King Théoden, Éowyn removes her guise as Dernhelm and kills the fell beast as well as its rider. The winged Wraiths would later join the Battle of the Black Gate and be engaged in battle by Gwaihir and his Great Eagles, only to flee at the command of Sauron when he sensed Frodo donning the Ring within Mount Doom. When the Ring was destroyed, the Fellbeasts, Nazgul and Sauron alike as well as all his creations, were unmade.
In the Films
In Peter Jackson's trilogy of movies based on The Lord of the Rings, the Fellbeasts are depicted as Wyverns (a two legged, flying serpentine creature that is similar to a Dragon); their heads appear more like a snake's and they don't have beaks, but rather are armed with sharp teeth and massive talons. Their role otherwise is much the same as in the novels. Fellbeasts were powerful creatures and were deadly offensive predators, especially with the Nazgûl on them. They could choose either to bite their prey or swoop down on them, scattering enemies apart or outright crushing them. If a Fell beast snatched a soldier, it could easily fly high into the air and drop its helpless victim to his death far below. In the Battle of Minas Tirith, the Fellbeasts were used by the Nazgul to smash the city's trebuchets and snatch soldiers off the ramparts before dropping them to their deaths far below. In addition, the Witch-king's Fellbeast was armored with a spiked helmet for close-quarter combat.
In Video Games
Fell Beasts appear in many of the Lord of the Rings video games, in which they are used by the Nazgul to swoop down upon and snatch their enemies. They also appear in The Lord of the Rings: War in the North, ridden by Sauron's lieutenant, Agandaur and his captain, Wulfrun. Both Fellbeasts are killed in the game by the great eagle, Beleram.