Nastily Exhausting Wizarding Test

N.E.W.T.s (Nastily Exhausting Wizarding Tests) are subject-specific exams that seventh-year wizards and witches at Hogwarts take to help them get certain jobs after graduation. For instance, the Ministry of Magic only accept Auror applicants with at least five N.E.W.T.s with the grade "Exceeds Expectations" or better. Not all wizards pass or even take the N.E.W.T.s, as they can find other jobs using their O.W.L. results. Fred and George Weasley, for example, were not bothered about taking the N.E.W.T.s and left Hogwarts in the middle of school-term (since their ambition was to open their joke shop, results were not an imperative in their opinion).

A student must have previously achieved an O.W.L. in the subject in order to move on to N.E.W.T.-level classes. Most Hogwarts Professors will accept an "Exceeds Expectations" in the student's O.W.L. for a class in order to allow them into the N.E.W.T.-level classes; however, some, such as Severus Snape, would only let students with an "Outstanding" in their O.W.L. pass through to his Potions N.E.W.T. class.

Aurors

 * Alastor Moody
 * Alice Longbottom
 * Frank Longbottom
 * Gawain Robards
 * John Dawlish
 * Kingsley Shacklebolt
 * Nymphadora Tonks
 * Proudfoot
 * Rufus Scrimgeour
 * Savage
 * Williamson

Others

 * Albus Dumbledore
 * Barty Crouch Jr.
 * Hermione Granger
 * Percy Weasley
 * Tom Marvolo Riddle
 * Most likely others who worked for the Ministry of Magic, such as Arthur Weasley and Mafalda Hopkirk and Dolores Umbridge.

Notable students who didn't pass N.E.W.T.S.

 * Harry Potter (didn't return to school for seventh year; went to work for the Ministry as an Auror).
 * Ron Weasley (didn't return to school for seventh year; went to work for the Ministry as an Auror).
 * Neville Longbottom (went to work for the Ministry as an Auror, then returned to Hogwarts as a professor).
 * Fred and George Weasley (left during the rule of Dolores Umbridge, before exams were over).
 * Cedric Diggory (murdered by Peter Pettigrew before the end of term)

Behind the scenes

 * The N.E.W.T. is comparable to the Muggle A-Levels given at the same stage of education in most of the UK and Commonwealth, the Advanced Placement exams given in the United States, the Higher School Certificate (or comparable certificates) given in Australia, or the International Baccalaureate Diploma Programme given worldwide.
 * Harry Potter, Ron Weasley, and Hermione Granger skipped the 1997–1998 school year, which would have been their final year, due to the reign of Lord Voldemort and their search for his Horcruxes. Presumably, Muggle-born students also missed their schooling that year. After the defeat of Voldemort, Hermione completed her education and took her N.E.W.T.s, while Harry became an Auror and Ron helped his brother George at Weasleys' Wizard Wheezes, and later became an Auror as well. Those who participated in the Battle of Hogwarts were given exemptions from usual Auror qualifications by Kingsley Shacklebolt due to their dueling experience.
 * Doing well on N.E.W.T.s is imperative to earning a position at the Ministry of Magic.
 * N.E.W.T.s are the highest level of examinations given at Hogwarts. It is unknown what system other wizarding schools such as Beauxbatons or Durmstrang use.

Notes and references
A.S.P.I.C.