Thestral

A Thestral is an unusual type of winged horse, invisible to those who have not witnessed death. Thestrals are considered highly unlucky by most wizards and, to those who have seen death, appear as carnivorous, skeletal horses with reptilian features.

History of Use
The carriages that transport Hogwarts students (other than first years) from the Hogwarts Express to the castle are drawn by Thestrals, but the invisibility of the creatures causes most students to assume that the carriages are guided magically, without the aid of draft animals. Harry Potter first saw the Thestrals at Hogwarts in September of 1995, after having witnessed the murder of Cedric Diggory the same June. J. K. Rowling explained that he hadn't seen them that June because he had not yet dealt with what he had witnessed.

In 1996, Harry, Hermione Granger, Ron Weasley, Ginny Weasley, Luna Lovegood, and Neville Longbottom flew to London atop the Thestrals in order to find Sirius Black, whom Harry believed to be in danger in the Ministry of Magic.

The Order of the Phoenix made use of Thestrals in the summer of 1997 during the flight from Little Whinging. They had six members take Polyjuice Potion to disguise themselves as Harry, and then the "seven Potters" and their protectors fled 4 Privet Drive to Order safehouses. Hermione Granger and Kingsley Shacklebolt flew on a Thestral, as did Bill Weasley and Fleur Delacour.

During the Battle of Hogwarts, Thestrals were seen attacking Lord Voldemort's giant soldiers from the air along with Buckbeak the hippogriff.

It can also be noted that the core of the Elder Wand was from the tail of a Thestral.

Known People who could see Thestrals by 1996
Presumably, after the Second Wizarding War, many students of Hogwarts could see Thestrals after witnessing a great many casualties in battle, including the death of Lord Voldemort himself.

Behind the scenes

 * Harry had the chance to witness at least two people die before the death of Cedric Diggory in Goblet of Fire. His mother was murdered by Lord Voldemort when he was one, and Professor Quirrell in his first year. Despite this, Harry is not able to see the Thestrals till the beginning of his fifth year. J. K. Rowling has explained this stating that he was in his crib when his mother was murdered, and passed out before Quirrel died. It's also plausible that when his parents died, Harry was too young to truly understand the concept of accepting someone's death. This creates a paradox in the films, since the first film shows Harry seeing Quirrell die.

Notes and references
Thestral