Theodore Nott (Slytherin, 1991-1998) is the son of the Death Eater Nott (PS7, OP26). Theodore is described as “weedy-looking” (OP26) and “a clever loner who does not feel the need to join gangs, including Malfoy’s” (JKR).
During Care of Magical Creatures class in fifth year, he is the “stringy” boy who can see the Thestrals, just like Harry, Neville, and Luna Lovegood. Since his father was an “elderly widower” it’s probable that Theodore was affected by “seeing” his mother’s death in some way (OP21, JKR).
Theodore’s father Nott was one of the first followers (or servants) of Lord Voldemort (HBP20). His father was also a friend of Lucius Malfoy and they both fought against the Order of the Phoenix at the Department of Mysteries (OP35). Injured during the battle, he was arrested with Lucius and sent to Azkaban, which is why neither Theodore Nott nor Draco Malfoy were invited by Professor Slughorn to join his Slug Club (HBP7). After that, Theodore and Draco seemed to form a bond as two outsiders, at least in Potions class, where they seemed to share a joke over Hermione being a Muggle-born, as well as the love potion Amortentia (HBP9).
After leaving school Theodore Nott is at least partly involved in handling illegal magical goods, including an Experimental Time-Turner which is confiscated from his house after a raid led by Harry Potter while head of the Department of Magical Law Enforcement. Theodore Nott is then held in custody by the Ministry of Magic (CC1.5, CC1.6, CC1.10).
Other canon notes and references
J.K. Rowling said she knows a great deal about Theodore Nott which she never put into the books, although she wrote a scene of Nott at Malfoy Manor talking about how Harry was able to defeat the Dark Lord.
. . . in this scene Theodore's father (the same Nott who was badly injured in the closing chapters of 'Order of the Phoenix') goes to visit Lucius Malfoy to discuss Voldemort-related business and we see Draco and Theodore alone in the garden having a talk of their own. I really liked the scene, firstly because it showed the Malfoys' home, and the difference between the place where Draco has grown up and number four, Privet Drive; then because we rarely see Draco talking to anybody he considers a real equal, and he is forced to see Theodore as such, because Theodore is just as pure-blooded as he is, and somewhat cleverer. Together these two Death Eaters' sons discuss Dumbledore's regime at Hogwarts and Harry Potter, with all sorts of stories that the Death Eaters tell about how this baby boy survived the Dark Lord's attack. (JKR - Edits).
Theodore is from the Greek "Theodros" or "God's gift." It is also the name of Harry's godson, Teddy Lupin (Wikipedia).
Nott is the Norse goddess of Night and the grandmother of Thor the thunder god (Wikipedia). Alternatively, the surname may be a variation of "Cnut" or more commonly "King Canute," the name of a King who ruled England, Denmark, and other Scandinavian lands referred to as the North Sea Empire (Wikipedia).
Played in the movies by Bronson Webb IMDB
Although JKR said Nott wasn't in Draco's gang, he is often shown together with them in the movies.
Fan Theory: JKR said she was interested in Theodore Nott and had lots of backstory on him, so of course fans believed he might become more important to the story as it went along. He was not supposed to be involved with Draco's gang, and was one of the students who could see Thestrals, along with Luna, Harry and Neville. So fans believed he might be clever enough to find some common ground with those in other houses, in spite of his father being a Death Eater. Unfortunately, this theory fizzled out when the arrest of Nott's father gave him even more in common Draco, and a bit of vendetta against Harry, who had named names of Death Eaters in the Quibbler. Nott was not the "good Slytherin" we were looking for, as far as we know (unless he grew up and moved past it, as Draco seems to have done).